Shares and Dividends

Find the market value of:

(i) 350, ₹ 100 shares at a premium of ₹ 8.

(ii) 240, ₹ 50 shares at a discount of ₹ 5.

Answer

(i) Given,

Face Value = ₹ 100

Premium = ₹ 8

Market Value per share = Face Value + Premium = ₹ 100 + ₹ 8 = ₹ 108.

∴ Total market value of 350 shares = 350 × ₹ 108 = ₹ 37,800.

Hence, the market value is ₹ 37,800.

(ii) Given,

Face Value = ₹ 50

Discount = ₹ 5

Market Value per share = Face Value - Discount = ₹ 50 - ₹ 5 = ₹ 45

∴ Total market value of 240 shares = 240 × 45 = ₹ 10,800.

Hence, the market value is ₹ 10,800.

Find the annual income from 450, ₹ 25 shares, paying 12% dividend.

Answer

Given,

Number of shares = 450

Face Value of 1 share = ₹ 25

Rate of dividend = 12%

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= $450 \times \dfrac{12}{100} \times 25$

= 450 × 3

= ₹ 1,350.

Hence, the annual income from the shares equal to ₹ 1,350.

Mr. Gupta invested ₹33000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%.

Find:

(i) the number of shares purchased by him.

(ii) his annual dividend.

Answer

(i) Money invested = ₹33000

N.V. of share = ₹100

M.V. = N.V + Premium

= ₹100 + $\dfrac{10}{100}$ × 100

= ₹100 + ₹10

= ₹110.

Number of shares = $\dfrac{\text{Money invested}}{\text{M.V}} = \dfrac{33000}{110} = 300$

Hence, no. of shares purchased = 300.

(ii) By formula,

Annual dividend = Number of shares × Rate of dividend × N.V.

= 300 × $\dfrac{12}{100}$ ×100

= ₹3600.

Hence, annual dividend = ₹3600.

A man invests ₹ 22,500 in ₹ 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate :

(i) the number of shares purchased;

(ii) the annual dividend received;

(iii) the rate of return he gets on his investment.

Answer

Given,

Investment = ₹ 22,500

Face Value = ₹ 50

Discount Rate = 10%

Discount = $\dfrac{10}{100} \times 50$ = ₹ 5

Market Value = Face Value - Discount = ₹ 50 - ₹ 5 = ₹ 45

Rate of dividend = 12%

(i) By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}}$

= $\dfrac{22,500}{45}$

= 500.

Hence, the number of shares purchased is 500.

(ii) By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

= $500 × \dfrac{12}{100} \times 50$

= ₹ 3,000.

Hence, the annual dividend received is ₹ 3,000.

(iii) By formula,

Rate of return = $\dfrac{\text{Income}}{\text{Investment}} \times 100$

= $\dfrac{3000}{22500} \times 100$

= 13.33%.

Hence, the rate of return is 13.33%.

Find the market price of 12%, ₹ 25 shares of a company which pays a dividend of ₹ 1,875 on an investment of ₹ 20,000.

Answer

Given,

Face Value = ₹ 25

Rate of dividend = 12%

Annual dividend = ₹ 1,875

Investment = ₹ 20,000

By formula,

Income from each share = Rate of div. × N.V. of 1 share

= $\dfrac{12}{100} \times 25$

= ₹ 3.

$\text{Number of shares bought} = \dfrac{\text{Total annual income}}{\text{Annual income from 1 share} }\\[1em] = \dfrac{1875}{3} \\[1em] = 625. \\[1em] \text {Market price per share} = \dfrac{\text{Investment}}{\text{Number of shares}} \\[1em] =\dfrac{20000}{625} \\[1em] = ₹ 32.$

Hence, the market price per share is ₹ 32.

Mr. Ram Gopal invested ₹ 8,000 in 7%, ₹ 100 shares at ₹ 80. After a year, he sold these shares at ₹ 75 each and invested the proceeds (including his dividend) in 18%, ₹ 25 shares at ₹ 41. Find :

(i) his dividend for the first year;

(ii) his annual income in the second year;

(iii) the percentage increase in his return on his original investment.

Answer

Given,

For initial investment,

Investment = ₹ 8,000

Face Value = ₹ 100

Market Value = ₹ 80

Dividend Rate = 7%

(i) By formula,

Number of shares = $\dfrac{ \text{Investment}}{ \text{Market value of each share}} = \dfrac{8000}{80}$ = 100

By formula,

Dividend for the first year = No. of shares × Rate of div. × N.V. of 1 share

$= 100 \times \dfrac{7}{100} \times 100$

= ₹ 700

Hence, dividend for the first year is ₹ 700.

(ii) Given,

Selling Price of each share = ₹ 75

Total sale value = Number of shares × Selling Price of each share = 100 × 75 = ₹ 7,500

Total proceeds = Total sale value + Dividend from first year

= ₹ 7,500 + ₹ 700 = ₹ 8,200.

He invested the proceeds in 18%, ₹ 25 shares at ₹ 41.

In second Investment :

Face Value = ₹ 25

Market Value = ₹ 41

Dividend Rate = 18%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8200}{41}$ = 200.

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= $200 \times \dfrac{18}{100} \times 25$

= ₹ 900.

Hence, Mr. Ram's annual income in the second year equals to ₹ 900.

(iii) Original annual income = ₹ 700

New annual income = ₹ 900

Increase in income = ₹ 900 - ₹ 700 = ₹ 200

Percentage increase = $\dfrac{\text{Increase in income}}{ \text{Initial investment}} \times 100$

= $\dfrac{200}{8000} \times 100$

= 2.5%

Hence, the percentage increase in return on original investment equals to 2.5%.

Amit Kumar invests ₹ 36,000 in buying ₹ 100 shares at ₹ 20 premium. The dividend is 15% per annum. Find :

(i) the number of shares he buys;

(ii) his yearly dividend;

(iii) the percentage return on his investment.

Give your answer correct to the nearest whole number.

Answer

Given,

Investment = ₹ 36,000

Face Value = ₹ 100

Premium = ₹ 20

Market Value = Face value + Premium = ₹ 100 + ₹ 20 = ₹ 120

Dividend Rate = 15%

(i) By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{36000}{120}$ = 300

Hence, Amit buys 300 shares.

(ii) By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

= $300 \times \dfrac{15}{100} \times 100$

= ₹ 4,500.

Hence, Amit's yearly dividend is ₹ 4,500.

(iii) By formula,

Percentage return = $\dfrac{\text{Income}}{\text{Investment}} \times 100$

= $\dfrac{4500}{36000} \times 100$

= 12.5% ≈ 13%.

Hence, the percentage return on investment equals to 13%.

Ajay owns 560 shares of a company. The face value of each share is ₹ 25. The company declares a dividend of 9%. Calculate :

(i) The dividend that Ajay will get;

(ii) The rate of interest on his investment, if Ajay had paid ₹ 30 for each share.

Answer

Given,

Number of shares = 560

Face Value = ₹ 25

Dividend Rate = 9%

(i) By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

= $560 \times \dfrac{9}{100} \times 25$

= ₹ 1,260.

Hence, the dividend that Ajay receives equals to ₹ 1,260.

(ii) Given,

Market value = ₹ 30

By formula,

Investment = Number of shares × Market value

= 560 × 30 = ₹ 16,800.

By formula,

Percentage return = $\dfrac{\text{Income}}{\text{Investment}} \times 100$

= $\dfrac{1260}{16800} \times 100$

= 7.5%.

Hence, the rate of interest (return) is 7.5%.

Mohan Lal invested ₹ 29,040 in 15%, ₹ 100 shares of a company quoted at a premium of 20%. Calculate :

(i) the number of shares bought by Mohan Lal;

(ii) his annual income from shares;

(iii) the percentage return on his investment.

Answer

Given,

Investment = ₹ 29,040

Face Value = ₹ 100

Premium Rate = 20%

Premium = $\dfrac{20}{100} \times 100$ = ₹ 20

Market Value = Face Value + Premium = ₹ 100 + ₹ 20 = ₹ 120

Dividend Rate = 15%

(i) By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{29040}{120}$ = 242.

Hence, Mohan Lal bought 242 shares.

(ii) By formula,

Annual income = Number of shares × Rate of dividend × N.V. of 1 share

= $242 \times \dfrac{15}{100} \times 100$

= ₹ 3,630.

Hence, the annual income from shares is ₹ 3,630.

(iii) By formula,

$\text{Percentage return} = \dfrac{\text{Income}}{\text{Investment}} \times 100$

Hence, the percentage return on investment equals to 12.5%.

A man invests ₹ 8,800 on buying shares of face value ₹ 100 each at a premium of 10%. If he earns ₹ 1,200 at the end of the year as dividend, find :

(i) the number of shares he has in the company,

(ii) the dividend percentage per share.

Answer

Given,

Investment = ₹ 8,800

Face Value = ₹ 100

Premium rate = 10%

Premium = $\dfrac{10}{100} \times 100$ = ₹ 10

Market Value = Face Value + Premium = ₹ 100 + ₹ 10 = ₹ 110

Dividend = ₹ 1,200

(i) Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8800}{110}$ = 80

Hence, the number of shares the man has in the company equals to 80.

(ii) By formula

Dividend per share = $\dfrac{\text{Total dividend}}{\text{Number of shares}} = \dfrac{1200}{80}$ = ₹ 15.

Dividend percentage per share = $\dfrac{15}{100} \times 100$ = 15%.

Hence, the dividend percentage per share is 15%.

A man invests a sum of money in ₹ 100 shares, paying 10% dividend and quoted at 20% premium. If his annual dividend from these shares is ₹ 560, calculate :

(i) his total investment,

(ii) the rate of return on his investment.

Answer

Given,

Rate of Dividend = 10%

Annual dividend = ₹ 560

Face Value = ₹ 100

Premium Rate = 20%

Premium = $\dfrac{20}{100} \times 100$ = ₹ 20

Market Value = Face Value + Premium = ₹ 120

(i) By formula,

$\text{Annual income from one share} = \dfrac{\text{Rate of Dividend}}{100} \times \text{Face Value of one share} \\[1em] = \dfrac{10}{100} \times 100 = ₹10 \\[1em] \text{Number of shares} = \dfrac{\text{ Annual income}}{\text{ Annual income from 1 share}} \\[1em] =\dfrac{560}{10} \\[1em] = 56.$

By formula,

Investment = Number of shares × Market value of each share

= 56 × 120

= ₹ 6,720.

Hence, his total investment is ₹ 6,720.

(ii) By formula,

$\text{Percentage return} = \dfrac{\text{Income}}{\text{Investment}} \times 100$

Hence, the rate of return on his investment is $8\dfrac{1}{3}$.

A man invests a sum of money in ₹ 25 shares, paying 12% dividend and quoted at ₹ 36. If his annual income from these shares is ₹ 720, calculate :

(i) his total investment,

(ii) the number of shares bought by him,

(iii) the percentage return on his investment.

Answer

Given,

Face Value = ₹ 25

Market Value = ₹ 36

Rate of Dividend = 12%

Annual Income = ₹ 720

(i) Let the man bought x shares.

By formula,

Annual Income = No. of shares × Rate of div. × N.V. of 1 share

$\Rightarrow 720 = x \times \dfrac{12}{100} \times 25 \\[1em] \Rightarrow 720 = 3x \\[1em] \Rightarrow x = \dfrac{720}{3} \\[1em] \Rightarrow x = 240.$

∴ No. of shares bought = 240

By formula,

Investment = Number of shares × Market value of each share

= 240 × 36

= ₹ 8,640.

Hence, the total investment equals to ₹ 8,640.

(ii) From part (i), we get :

No. of shares bought = 240

Hence, the number of shares bought equals to 240.

(iii) By formula,

$\text{Percentage return} = \dfrac{\text{Income}}{\text{Investment}} \times 100$

Hence, the percentage return on his investment is $8\dfrac{1}{3}$.

A man buys 250, ten-rupee shares each at ₹12.50. If the rate of dividend is 7%, find the :

(i) dividend he receives annually.

(ii) percentage return on his investment.

Answer

(i) Nominal Value of 1 share = ₹10

Market Value of 1 share = ₹12.50

Number of shares purchased = 250

Nominal Value of 250 shares = 250 x 10 = ₹2500

Rate of dividend = 7%

∴ Dividend received = 7% of 2500

= $\dfrac{7}{100} \times 2500$

= ₹175.

Hence, annual dividend = ₹175.

(ii) Amount Invested = No. of shares x Market Value

= 250 x 12.50

= ₹3125

$\text{Return percentage } = \dfrac{\text{Dividend received}}{\text{Investment}} \times 100 \\[1em] = \dfrac{175}{3125} \times 100 \\[1em] = \dfrac{17500}{3125} \\[1em] = 5.6$

Hence, return percentage = 5.6%.

Divide ₹ 35,400 into two parts such that if one part is invested in 9%, ₹ 100 shares at 4% discount, and the other in 12%, ₹ 50 shares at 8% premium, the annual incomes are equal.

Answer

Given,

Total Investment = ₹ 35,400

Let the investments be ₹ x and ₹ 35,400 - x.

For the first investment,

Face Value = ₹ 100

Discount Rate = 4%

Discount = 4% of 100 = $\dfrac{4}{100} \times 100 = ₹ 4$

Market Value = Face Value - Discount = ₹ 96

Dividend Rate = 9%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{x}{96}$

$\text{Income from first part} = \text{No. of shares × Rate of div. × N.V. of 1 share}\\[1em] = \dfrac{x}{96} \times \dfrac{9}{100} \times {100}\\[1em]= \dfrac{9x}{96} \\[1em] = \dfrac{3x}{32}.$

For the second investment,

Face Value = ₹ 50

Premium Rate = 8%

Premium = 8% of 50 = $\dfrac{8}{100} \times 50$ = ₹ 4

Market Value = Face Value + Premium = ₹ 54

Dividend Rate = 12%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{35400 - x}{54}$

$\text{Income from second part} =\text{ No. of shares × Rate of div. × N.V. of 1 share}\\[1em] =\dfrac{35400 - x}{54} \times \dfrac{12}{100} \times 50\\[1em] = \dfrac{35400 - x}{54} \times 6 \\[1em] = \dfrac{35400 - x}{9}.$

Given,

Income from the both the investments are equal.

$\therefore \dfrac{3x}{32} = \dfrac{35400 - x}{9} \\[1em] \Rightarrow 9 \times 3x = 32(35400 - x) \\[1em] \Rightarrow 27x = 1132800 - 32x \\[1em] \Rightarrow 27x + 32x = 1132800 \\[1em] \Rightarrow 59x = 1132800 \\[1em] \Rightarrow x = \dfrac{1132800}{59} \\[1em] \Rightarrow x = ₹ 19,200.$

First part = x = ₹ 19,200

Second part = ₹ (35,400 - x) = ₹ 35,400 - ₹ 19,200 = ₹ 16,200

Hence, first part = ₹ 19,200 and second part = ₹ 16,200.

Divide ₹ 50,760 into two parts such that if one part is invested in 8%, ₹ 100 shares at 8% discount and the other in 9%, ₹ 100 shares at 8% premium, the annual incomes from both the investments are equal.

Answer

Given,

Total Investment = ₹ 50,760

Let the first part invested in 8%, ₹ 100 shares at 8% discount be ₹ x.

Second part = ₹ 50,760 − ₹ x

For the first investment :

Face Value = ₹ 100

Discount Rate = 8%

Discount = 8% of 100 = $\dfrac{8}{100} \times 100$ = ₹ 8

Market Value = Face Value - Discount = ₹ 92

Dividend Rate = 8%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{x}{92}$

By formula,

$\text{Income from first part} =\text{ No. of shares × Rate of div. × N.V. of 1 share}\\[1em] = \dfrac{x}{92} \times \dfrac{8}{100} \times {100}\\[1em] = \dfrac{8x}{92}.$

For the second investment :

Face Value = ₹ 100

Premium Rate = 8%

Premium = 8% of 100 = $\dfrac{8}{100} \times 100$ = ₹ 8

Market Value = Face Value + Premium = ₹ 108

Dividend Rate = 9%

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{50760 - x}{108}$

By formula,

$\text{Income from second part} = \text{No. of shares × Rate of div. × N.V. of 1 share}\\[1em] = \dfrac{50760 - x}{108} \times \dfrac{9}{100} \times {100} \\[1em] = \dfrac{50760 - x}{108} \times 9$

Given,

Income from the both the investments are equal.

$\therefore \dfrac{8x}{92} = \dfrac{50760 - x}{108} \times 9 \\[1em] \Rightarrow 8 \times 108x = 9 \times 92(50760 - x) \\[1em] \Rightarrow 864x = 828(50760 - x) \\[1em] \Rightarrow 864x = 42029280 - 828x \\[1em] \Rightarrow 864x + 828x = 42029280 \\[1em] \Rightarrow 1692x = 42029280 \\[1em] \Rightarrow x = \dfrac{42029280}{1692} = ₹24,840.$

First part = x = ₹ 24,840

Second part = ₹ (50,760 − x) = ₹ 25,920

Hence, first part = ₹ 24,840 and second part = ₹ 25,920.

Which is the better investment:

(10%, ₹ 100 shares at ₹ 120) or (8%, ₹ 100 shares at ₹ 72)?

Answer

Since,

Profit% on M.V. = Dividend% on N.V.

In first case,

P% on ₹ 120 = 10% on ₹ 100

$\Rightarrow \dfrac{P}{100} \times 120 = \dfrac{10}{100} \times 100 \\[1em] \Rightarrow 120P = 1000 \\[1em] \Rightarrow P = \dfrac{1000}{120} = 8.33$

In second case,

P% on ₹ 72 = 8% on ₹ 100

$\Rightarrow \dfrac{P}{100} \times 72 = \dfrac{8}{100} \times 100 \\[1em] \Rightarrow 72P = 800 \\[1em] \Rightarrow P = \dfrac{800}{72} = 11.11$

Hence, 8% ₹ 100 shares at ₹ 72 is the better investment.

Which is the better investment:

(12%, ₹ 20 shares at ₹ 16) or (15%, ₹ 20 shares at ₹ 24)?

Answer

Since,

Profit% on M.V. = Dividend% on N.V.

In first case,

P% on ₹ 16 = 12% on ₹ 20

$\Rightarrow \dfrac{P}{100} \times 16 = \dfrac{12}{100} \times 20 \\[1em] \Rightarrow P \times 16 = 240 \\[1em] \Rightarrow P = \dfrac{240}{16} = 15$

In second case,

P% on ₹ 24 = 15% on ₹ 20

$\Rightarrow \dfrac{P}{100} \times 24 = \dfrac{15}{100} \times 20 \\[1em] \Rightarrow P \times 24 = 15 \times 20 \\[1em] \Rightarrow P = \dfrac{300}{24} = 12.5$

Hence, 12% ₹ 20 shares at ₹ 16 is the better investment.

Ashish bought 4,500, ₹ 10 shares paying 12% per annum. He sold them when the price rose to ₹ 23 and invested proceeds in ₹ 25 shares paying 10% per annum at ₹ 18. Find the change in his annual income.

Answer

Given,

Initial Investment,

Number of shares = 4,500

Face Value = ₹ 10

Dividend Rate = 12%

By formula,

Initial Annual Income = No. of shares × Rate of div. × N.V. of 1 share

= $4500 \times \dfrac{12}{100} \times 10$

= ₹ 5,400.

Given,

Ashish sold the shares when the price rose to ₹ 23.

Selling Price per share = ₹ 23

Sale Amount = No.of Shares × S.P.

= 4500 × ₹ 23

= ₹ 1,03,500

For the new Investment :

Face Value = ₹ 25

Market Value = ₹ 18

Dividend Rate = 10%

By formula,

$\text{Number of shares} = \dfrac{\text{Investment}}{\text{ Market value of each share}} \\[1em] = \dfrac{103500}{18} \\[1em] = 5750. \\[1em] \text{New Annual Income} = \text{No. of shares} \times \text{Rate of div.} \times \text{N.V. of 1 share}\\[1em] = 5750 \times \dfrac{10}{100} \times 25 \\[1em] = ₹ 14,375.$

Change in Income = New Annual Income - Initial Annual Income

= ₹ 14,375 - ₹ 5,400 = ₹ 8,975.

Hence, Ashish's annual income increased by ₹ 8,975.

Amit owns 1500, ₹ 25 shares of a company which declares a dividend of 14%. He sells the shares at ₹ 40 each and invests the proceeds in 8%, ₹ 100 shares at ₹ 80. What is the change in his annual dividend income ?

Answer

Given,

Initially,

Number of shares = 1500

Face Value = ₹ 25

Dividend Rate = 14%

Initial Annual Income = No. of shares × Rate of div. × N.V. of 1 share

$= 1500 \times \dfrac{14}{100} \times 25$

= 750 × 7

= ₹ 5,250.

Selling price per share = ₹ 40

By formula,

Sale Amount = No. of Shares × Selling price per share = 1500 × 40 = ₹ 60,000.

For new Investment,

Face Value = ₹ 100

Dividend Rate = 8%

Market Value = ₹ 80

By formula,

$\text{Number of shares} = \dfrac{\text{ Investment }}{\text{ Market value of each share}} \\[1em] = \dfrac{60000}{80} \\[1em] = 750. \\[1em] \text{New Annual Income} = \text{No. of shares} \times \text{Rate of div.} \times \text{N.V. of 1 share}\\[1em] = 750 \times \dfrac{8}{100} \times 100\\[1em] = ₹ 6,000.$

Change in Income = New Annual Income - Initial Annual Income = 6,000 - 5,250 = ₹ 750.

Hence, Amit's annual dividend income increases by ₹ 750.

Vimal sold a certain number of ₹ 20 shares paying 8% dividend at ₹ 18 and invested the proceeds in ₹ 10 shares paying 12% dividend at 50% premium (i.e. ₹ 15). If his annual income decreases by ₹ 120, find the number of shares sold by Vimal.

Answer

Let the number of shares Vimal sold be x.

For initial shares,

N.V. = ₹ 20

Rate of dividend = 8%

By formula,

Annual income (from first investment) = No. of shares × Rate of div. × N.V. of 1 share

$= x \times \dfrac{8}{100} \times 20 = \dfrac{8x}{5}$

S.P. of each share = ₹ 18.

Amount obtained on selling shares = S.P × No. of shares = ₹ 18x.

The proceeds he invested in ₹ 10 shares at ₹ 15, paying 12% dividend.

N.V. = ₹ 10

M.V. = ₹ 15

No. of shares bought by man = $\dfrac{\text{Amount invested}}{\text{M.V. of each share}} = \dfrac{18x}{15} = \dfrac{6x}{5}.$

By formula,

Annual income (from second investment) = No. of shares × Rate of div. × N.V. of 1 share

$= \dfrac{6x}{5} \times \dfrac{12}{100} \times 10$

$= \dfrac{720x}{500} = \dfrac{36x}{25}$.

Given, decrease in income = ₹ 120

$\therefore \dfrac{8x}{5} - \dfrac{36x}{25} = 120 \\[1em] \Rightarrow \dfrac{40x - 36x}{25} = 120 \\[1em] \Rightarrow \dfrac{4x}{25} = 120 \\[1em] \Rightarrow x = \dfrac{120 \times 25}{4} \\[1em] \Rightarrow x = 750.$

Hence, Vimal sold 750 shares.

₹100 shares of a company giving 10% dividend are selling at ₹150. Mr. Saha invests ₹ 18,000 to buy these shares. He sells 80% of his shares after one year. Find :

(i) the number of shares he purchased.

(ii) the number of shares he sold.

(iii) his annual income from the remaining 20% shares he still holds.

Answer

(i) Given,

Total investment = ₹ 18,000

Market value = ₹ 150

N.V = ₹ 100

By formula,

⇒ Total investment = Number of shares × Market value of one share

⇒ 18000 = Number of shares × 150

⇒ Number of shares = $\dfrac{18000}{150}$

⇒ Number of shares = 120.

Hence, the number of shares Mr.Saha purchased = 120.

(ii) Number of shares sold by Mr Saha = 80% of 120

= $\dfrac{80}{100} \times 120$

= 0.8 × 120

= 96.

Hence, the number of shares Mr.Saha sold = 96.

(iii) Number of shares remaining = Total no. of shares - No. of shares sold = 120 - 96 = 24.

By formula,

Annual income = Number of shares × Rate of dividend × N.V. of 1 share

= 24 × $\dfrac{10}{100} \times 100$

= ₹ 240.

Hence, annual income from remaining shares = ₹ 240.

Deepak invested in ₹ 25 shares of a company paying 12% dividend. If he received 10% on his investment, at what price did he buy each share?

Answer

Given,

Face Value = ₹ 25

Dividend Rate = 12%

Return percentage = 10%

Let M.V. be ₹ x.

By formula,

Rate of dividend × N.V. = Profit (return) % × M.V.

$\therefore \dfrac{12}{100} \times 25 = \dfrac{10}{100} \times x \\[1em] \Rightarrow 12 \times 25 = 10x \\[1em] \Rightarrow x = \dfrac{300}{10}\\[1em] \Rightarrow x =₹\ 30.$

Hence, Deepak bought each share at ₹ 30.

At what price should a 10%, ₹ 25 share be quoted when money is worth 8%?

Answer

Given,

Face Value = ₹ 25

Dividend Rate = 10%

Return percentage = 8%

Let M.V. be ₹ x.

By formula,

Rate of dividend × N.V. = Profit (return) % × M.V.

$\therefore \dfrac{10}{100} \times 25 = \dfrac{8}{100} \times x \\[1em] \Rightarrow x = \dfrac{250}{8}\\[1em] \Rightarrow x = ₹ 31.25.$

Hence, the share should be quoted at ₹ 31.25.

How much should a man invest in ₹ 25 shares selling at ₹ 36 to obtain annual income of ₹ 1,500, if dividend declared is 12% ?

Answer

Given,

Face Value = ₹ 25

Market Value = ₹ 36

Dividend Rate = 12%

Required annual income = ₹ 1,500

Let no. of shares sold be ₹ x.

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$\Rightarrow 1500 = x \times \dfrac{12}{100} \times 25 \\[1em] \Rightarrow x = \dfrac{1500 \times 100}{25 \times 12} \\[1em] \Rightarrow x = 500.$

By formula,

Investment = No. of shares × Market value of each share

= 500 × 36

= ₹ 18,000.

Hence, the man should invest ₹ 18,000.

How much should a man invest in ₹ 50 shares selling at ₹ 60 to obtain an income of ₹ 450, if the rate of dividend declared is 10% ? Also, find his yield percent, to the nearest whole number.

Answer

Given,

Face Value = ₹ 50

Market Value = ₹ 60

Dividend Rate = 10%

Required Annual Income = ₹ 450

Let no. of shares sold be x.

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$\Rightarrow 450 = x \times \dfrac{10}{100} \times 50 \\[1em] \Rightarrow 450 = 5x \\[1em] \Rightarrow x = \dfrac{450}{5} = 90.$

Investment = No. of shares × Market value of each share

= 90 × 60 = ₹ 5,400.

By formula,

Yield % = $\dfrac{\text{Income}}{\text{Investment}} \times 100$

= $\dfrac{450}{5400} \times 100$ = 8.33% ≈ 8%.

Hence, the man should invest ₹ 5,400 and the yield percent is 8%.

By investing ₹ 11,440 in a company paying 10% dividend, an annual income of ₹ 520 is received. What is the market value of each ₹ 50 share?

Answer

Given,

Investment = ₹ 11,440

Annual Income = ₹ 520

Face Value = ₹ 50

Dividend Rate = 10%

Let market value of each share be ₹ x.

$\text{No. of share} = \dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{11440}{x}$

By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

$\therefore 520 = \dfrac{11440}{x} \times \dfrac{10}{100} \times 50\\[1em] \Rightarrow x = \dfrac{11440 \times 5}{520} \\[1em] \Rightarrow x = ₹ 110$

Hence, the market value of each share is ₹ 110.

A man invests ₹ 4,500 in shares of a company which is paying 7.5% dividend. If ₹ 100 shares are available at a discount of 10%, find :

(i) number of shares he purchases;

(ii) his annual income.

Answer

Given,

Investment = ₹ 4,500

Face Value = ₹ 100

Discount Rate = 10%

Discount = $\dfrac{10}{100} \times 100 = ₹\ 10$

Market Value = Face Value - Discount = ₹ 90.

Dividend Rate = 7.5%

(i) By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{4500}{90} = 50$

Hence, the number of shares purchased equals to 50.

(ii) By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

$\therefore \text{Annual dividend} = 50 \times \dfrac{7.5}{100} \times 100$

= 50 × 7.5

= ₹ 375

Hence, his annual income is ₹ 375.

Sachin invests ₹ 8,500 in 10%, ₹ 100 shares at ₹ 170. He sells the shares when the price of each share rises by ₹ 30. He invests the proceeds in 12%, ₹100 shares at ₹ 125. Find :

(i) the sale proceeds;

(ii) the number of ₹ 125 shares he buys;

(iii) the change in his annual income.

Answer

(i) Given,

Initially,

Investment = ₹ 8,500

Dividend rate = 10%

Face value = ₹ 100

Market value = ₹ 170

By formula,

$\text{No. of shares} = \dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8500}{170} = 50$

Given, shares are sold when price rises to ₹ 30,

Selling price = 170 + 30 = ₹ 200

By formula,

Sale proceeds = No. of shares × Sale Price

= 50 × 200

= ₹ 10,000.

Hence, sale proceeds = ₹ 10,000.

(ii) Given, the proceeds are invested in 12%, ₹ 100 shares at ₹ 125.

Investment = ₹ 10,000

Face value = ₹ 100

Market value = ₹ 125

Dividend rate = 12%

By formula,

No. of shares = $\dfrac{\text{ Investment }}{\text{ Market value of each share}} = \dfrac{10000}{125} = 80$

Hence, Sachin buys 80, ₹ 125 shares.

(iii) Annual income = No. of shares × Rate of div. × N.V. of 1 share

In first case,

Annual income = 50 × $\dfrac{10}{100} \times 100$ = ₹ 500.

In second case,

Annual income = 80 × $\dfrac{12}{100} \times 100$ = ₹ 960.

Change in income = 960 - 500 = ₹ 460.

Hence, the change in his annual income is ₹ 460.

A company with 500 shares of nominal value ₹ 120 declares an annual dividend of 15%. Calculate :

(i) the total amount of dividend paid by the company;

(ii) annual income of Mr. Sharma who holds 80 shares of the company;

If the return percent of Mr. Sharma from his shares is 10%, find the market value of each share.

Answer

Given,

Total number of shares = 500

Nominal Value (Face Value) = ₹ 120

Dividend Rate = 15%

(i) By formula,

Total dividend = Total number of shares × Rate of div. × N.V. of 1 share

∴ Total dividend = $500 \times \dfrac{15}{100} \times 120$ = ₹ 9,000.

Hence, the total amount of dividend paid by the company is ₹ 9,000.

(ii) Given,

Mr. Sharma holds 80 shares.

By formula,

Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

∴ Annual dividend = $80 \times \dfrac{15}{100} \times 120$ = ₹ 1,440

Hence, Mr. Sharma's annual income is ₹ 1,440.

Given,

The return percent of Mr. Sharma from his shares is 10%

Let the market value of shares be ₹ x.

By formula,

Rate of dividend × N.V. = Profit (return) % × M.V

$\therefore \dfrac{15}{100} \times 120 = \dfrac{10}{100} \times x \\[1em] \Rightarrow 15 \times 120 = 10x \\[1em] \Rightarrow x = \dfrac{1800}{10}\\[1em] \Rightarrow x = ₹\ 180.$

Hence, the market value of each share is ₹ 180.

A man bought ₹200 shares of a company at 25% premium. If he received a return of 5% on his investment. Find the :

(i) market value

(ii) dividend percent declared

(iii) number of shares purchased, if annual dividend is ₹1,000.

Answer

For one share:

Face value = ₹200

Premium = 25% of Face value

= $\dfrac{25}{100} \times 200$

= ₹50

(i) By formula,

M.V. = Face value + Premium

= ₹200 + ₹50

= ₹250.

Hence, market Value = ₹ 250.

(ii) Given,

Return = 5%

Return on 1 share = $\dfrac{5}{100} \times 250$

= ₹ 12.50

By formula,

Dividend earned = No. of shares × rate of dividend × F.V. of 1 share

Let rate of dividend be r%.

Substituting values we get :

⇒ 12.50 = 1 × $\dfrac{r}{100}$ × 200

⇒ r = $\dfrac{12.50}{200} \times 100$

⇒ r = 6.25%

Hence, dividend percent = 6.25%.

(iii) By formula,

Annual dividend = Number of shares × Dividend% × Face value of 1 share

⇒ 1000 = Number of shares × $\dfrac{6.25}{100}$ × 200

⇒ 1000 = Number of shares × 12.5

⇒ Number of shares = $\dfrac{1000}{12.5}$ = 80.

Hence, number of shares purchased = 80.

Ms. Kaur invested ₹ 8,000 in buying ₹100 shares of a company paying 6% dividend at ₹ 80. After a year, she sold these shares at ₹75 each and invested the proceeds including the dividend received during the first year in buying ₹ 20 shares, paying 15% dividend at ₹ 27 each. Find the :

(i) dividend received by her during the first year.

(ii) number of shares purchased by her using the total proceeds.

Answer

(i) Given,

For initial investment,

Investment = ₹ 8,000

Face Value = ₹ 100

Market Value = ₹ 80

Dividend Rate = 6%

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8000}{80}$ = 100

By formula,

Dividend for the first year = No. of shares × Rate of div. × N.V. of 1 share

= 100 × $\dfrac{6}{100}$ × 100

= ₹ 600

Hence, dividend for first year = ₹ 600.

(ii) Given,

Number of shares sold = 100

Selling price per share = ₹ 75

Proceeds from sale = Number of shares × selling price

= 100 × 75

= ₹ 7,500

Total proceeds = Proceeds from sale + Dividend received = 7500 + 600 = ₹ 8,100

Total investment = ₹ 8,100

Market value per share = ₹ 27

Number of new shares = $\dfrac{\text{Investment}}{\text{Market value of each share}} = \dfrac{8100}{27}$ = 300

Hence, number of shares purchased by Ms. Kaur = 300.

The annual profit distributed among share holders is called :

1. Nominal value

2. Market value

3. Dividend

4. Face value

Answer

Dividend is the money shared from profits among the shareholders.

Hence, Option 3 is the correct option.

The value of a share printed on the share certificate is called :

1. Nominal value

2. Market value

3. Discount

4. Below par

Answer

The value printed on a share certificate is called the nominal value (also known as the face value). Nominal value is the official value printed on the certificate.

Hence, Option 1 is the correct option

The shares of different companies can be bought or sold in the market through stock-exchange. The price at which the share is sold or purchased is called its :

1. Face value

2. Market value

3. Par value

4. Nominal value

Answer

Market value is the price at which a share is currently bought or sold in the stock market.

Hence, Option 2 is the correct option.

A share is said to be at ..............., if its market value is the same as its face value.

1. Premium

2. Discount

3. Par

4. Nominal value

Answer

If a share's market value (current price in the market) is exactly equal to its face value (the value printed on the share certificate), then the share is said to be at par.

Hence, Option 3 is the correct option.

A share is said to be at premium, if market value is ............... than its face value.

1. More

2. Less

3. Same

4. Equal

Answer

If a share’s market value is more than its face value, then the share is said to be at premium.

Hence, Option 1 is the correct option.

The face value of a share :

1. Changes every year

2. Changes from time to time

3. Always remains the same

4. None of these

Answer

The face value of a share is the original value printed on the share certificate when it's issued. It’s like the label price and does not change with market conditions.

Hence, Option 3 is the correct option.

Dividend is always paid on the ............... of a share.

1. Market value

2. Face value

3. Investment

4. Dividend

Answer

A dividend is the portion of a company’s profit that is given to its shareholders. It is always calculated based on the face value, not on how much the shareholder paid or how much the share is currently worth in the market

Hence, Option 2 is the correct option.

The market value of a share :

1. Never changes

2. Changes from time to time

3. Changes every month

4. None of these

Answer

The market value of a share is the price at which it is currently being bought or sold in the stock market. This value depends on factors like company performance, demand, economic trends and so changes from time to time.

Hence, Option 2 is the correct option.

Number of shares held by a person =

1. $\dfrac{\text{Total Nominal Value}}{\text{Face Value of 1 share}}$

2. $\dfrac{\text{Total Market Value}}{\text{Face Value of 1 share}}$

3. $\dfrac{\text{Dividend}}{\text{Face Value of 1 share}}$

4. $\dfrac{\text{Dividend}}{\text{Investment}} \times 100$

Answer

$\text{Number of shares}=\dfrac{\text{Total Nominal Value}}{\text{Face Value of 1 share}}$

Hence, Option 1 is the correct option.

Dividend =

1. Number of shares × N.V

2. Number of shares × M.V

3. $\text{Face Value} \times \text{No. of shares} \times \dfrac{\text{Rate of Dividend}}{100}$

4. None of these

Answer

By formula,

Dividend = $\text{Face Value} \times \text{No. of shares} \times \dfrac{\text{Rate of Dividend}}{100}$

Hence, Option 3 is the correct option.

Rate of return on Investment =

1. $\dfrac{\text{Investment}}{\text{Dividend}}$

2. $\dfrac{\text{Dividend}}{\text{Investment}}$

3. $\dfrac{\text{Dividend}}{\text{Investment}} \times 100$

4. $\dfrac{\text{Investment}}{\text{Dividend}} \times 100$

Answer

By formula,

Rate of return on Investment = $\dfrac{\text{Dividend}}{\text{Investment}} \times 100$

Hence, Option 3 is the correct option.

$\dfrac{ \text{Investment}}{ \text{Sale proceeds}} =$

1. Number of shares × M.V

2. Number of shares × N.V

3. Face Value × No. of shares × Rate of Dividend

4. $\dfrac{ \text{Dividend}}{ \text{Investment}}$

Answer

$\dfrac{ \text{Investment}}{ \text{Sale proceeds}} =$ Number of shares × M.V

Hence, Option 1 is the correct option.

Annual Income =

1. Number of shares × Face Value

2. Number of shares × rate of dividend × Face value of 1 share

3. Number of shares × Market value × Face value

4. MV × NV × 100

Answer

By formula,

Annual Income = Number of shares × rate of dividend × Face value of 1 share

Hence, Option 2 is the correct option.

A man invested in a company paying 12% dividend on its share. If the percentage return on his investment is 10%, then the shares are:

1. at par

2. below par

3. above par

4. cannot be determined

Answer

Given,

Dividend rate = 12% of face value.

So, if face value = ₹100, dividend = ₹12.

Return = 10%

By formula,

Return % = $\dfrac{\text{Dividend on one share}}{\text{Investment on one share}} \times 100$

Investment on one share equals to the market value of the share.

Substituting values we get :

$\Rightarrow 10 = \dfrac{\text{12}}{\text{Market value}} \times 100 \\[1em] \Rightarrow \text{Market value} = \dfrac{12}{10} \times 100 \\[1em] \Rightarrow \text{Market value} = ₹120.$

Since market value > face value, the shares are said to be above par.

Hence, option 3 is the correct option.

If a share of ₹ 125 is selling at ₹ 96, then it is said to be selling at ₹ 29 :

1. Below par

2. At par

3. Above par

4. Premium

Answer

Given,

Face Value = ₹ 125

Market Value = ₹ 96

Discount = Face Value - Market Value = 125 - 96 = ₹ 29

This means the share is being sold at a discount of ₹ 29, which is also known as being sold below par.

Hence, Option 1 is the correct option.

If Kabir invests ₹ 10,320 on ₹ 100 shares at a discount of ₹ 14, then the number of shares he buys is :

1. 110

2. 120

3. 150

4. 100

Answer

Given,

Investment = ₹ 10,320

Face Value = ₹ 100

Discount = ₹ 14

Market Value = Face Value - Discount = 100 - 14 = ₹ 86

By formula,

$\text{Number of shares} = \dfrac{ \text{ Investment }}{ \text{ Market value}}\\[1em] = \dfrac{10320}{86}\\[1em] = 120.$

Hence, Option 2 is the correct option.

Shahrukh has some shares of ₹ 50 of a company paying 15% dividend. If his annual income is ₹ 3,000, then the number of shares he possesses is :

1. 400

2. 600

3. 800

4. 200

Answer

Given,

Face Value = ₹ 50

Dividend Rate = 15%

Annual Income = ₹ 3,000

Let the number of shares be x.

By formula,

⇒ Annual dividend = No. of shares × Rate of div. × N.V. of 1 share

⇒ 3000 = x × $\dfrac{15}{100}$ × 50

⇒ x = $\dfrac{3000 \times 100}{15 \times 50}$

⇒ x = 200 × 2

⇒ x = 400

Hence, Option 1 is the correct option.

If Kiran invests ₹ 19200 on ₹ 50 shares at a premium of 20%, then the number of shares she buys is :

1. 640

2. 160

3. 320

4. 240

Answer

Given,

Investment = ₹ 19,200

Face Value = ₹ 50

Premium Rate = 20%

Premium = 20% of 50 = $\dfrac{20}{100}$ ×50 = ₹ 10

Market Value = Face Value + Premium = 50 + 10 = ₹ 60

By formula,

Number of shares = $\dfrac{\text{Investment}}{\text{Market Value of each share}} = \dfrac{19200}{60}$ = 320.

Hence, Option 3 is the correct option.

The sum invested to purchase 15 shares of a company of nominal value ₹ 75 available at a discount of 20% is:

1. ₹ 60

2. ₹ 90

3. ₹ 1350

4. ₹ 900

Answer

N.V. = ₹ 75

Discount = 20%

M.V. = ₹ 75 - $\dfrac{20}{100} \times 75$

= ₹ 75 - ₹ 15

= ₹ 60.

Cost of 15 shares = 15 × ₹ 60 = ₹ 900.

Hence, Option 4 is the correct option.

Varun possesses 600 shares of ₹ 25 of a company. If the company announces a dividend of 8%, then his annual income is:

1. ₹ 600

2. ₹ 1,200

3. ₹ 480

4. ₹ 120

Answer

Given,

Number of shares = 600

Face Value = ₹ 25

Dividend rate = 8%

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= 600 × $\dfrac{8}{100}$ × 25 = ₹ 1,200.

Hence, Option 2 is the correct option.

A man invests ₹ 24,000 on ₹ 60 shares at a discount of 20%. If the dividend declared by the company is 10%, then his annual income is :

1. ₹ 2,880

2. ₹ 1,500

3. ₹ 3,000

4. None of these

Answer

Given,

Investment = ₹ 24,000

Face Value = ₹ 60

Dividend rate = 10%

Discount = 20% of 60 = $\dfrac{20}{100} \times 60$ = ₹ 12

Market Value = Face Value - Discount = 60 - 12 = ₹ 48.

By formula,

$\text{Number of shares} = \dfrac{\text{ Investment }}{\text{ Market value of each share}}\\[1em] = \dfrac{24000}{48} \\[1em] = 500. \\[1em] \text{Annual dividend} = \text{No. of shares} \times \text{Rate of div.} \times \text{ N.V. of 1 share}\\[1em] = 500 \times \dfrac{10}{100} \times 60 \\[1em] = ₹\ 3,000.$

Hence, Option 3 is the correct option.

Amit invested a certain sum of money in ₹ 100 shares, paying a 7.5% dividend. The rate of return on his investment is 10%. The money invested by Amit to purchase 10 shares is :

1. ₹ 250

2. ₹ 750

3. ₹ 900

4. ₹ 1100

Answer

Let ₹ P be the price per share.

Amit brought 10 shares, so total investment = ₹ 10P

Dividend = 7.5%

Dividend per share = $\dfrac{7.5}{100} \times 100$ = ₹ 7.5

Total dividend = ₹ 7.5 × 10 = ₹ 75.

Rate of return = 10%

By formula,

Rate of return × Investment = Dividend

$\Rightarrow 10$

Total investment = 10P = 10 × ₹75 = ₹750.

Hence, Option 2 is the correct option.

₹ 25 shares of a company are selling at ₹ 20. If the company is paying a dividend of 12%, then the rate of return is :

1. 10%

2. 18%

3. 15%

4. 12%

Answer

Given,

Face Value = ₹ 25

Market Value = ₹ 20

Dividend rate = 12%

Let the rate of return be x%,

By formula,

Rate of dividend × N.V. = Profit (return) % × M.V.

$\therefore \dfrac{12}{100} \times 25 = \dfrac{\text{x}}{100} \times 20\\[1em] \Rightarrow 12 \times 25 = 20x \\[1em] \Rightarrow \text{x} = \dfrac{300}{20}\\[1em] \Rightarrow \text{x} = 15$

∴ Rate of return = 15%.

Hence, Option 3 is the correct option.

₹ 40 shares of a company are selling at 25% premium. If Mr. Wasim wants to buy 280 shares of the company, then the investment required by him is :

1. ₹ 14,000

2. ₹ 16,800

3. ₹ 8,400

4. ₹ 10,000

Answer

Given,

Face Value = ₹ 40

Premium rate = 25%

Premium = 25% of 40 = $\dfrac{25}{100} \times 40$ = ₹ 10

Number of shares = 280

Market Value = Face Value + Premium = 40 + 10 = ₹ 50

By formula,

Investment = Number of shares × Market Value of each share

= 280 × 50 = ₹ 14,000.

Hence, Option 1 is the correct option.

Percentage return on ₹100, 12% share of a company bought at 4% discount is:

1. 10%

2. 12%

3. 12.5%

4. 16%

Answer

Given,

Face value = ₹ 100

Discount = 4%

Discount amount = 4% of face value

= $\dfrac{4}{100} \times 100$

= ₹ 4.

Dividend rate = 12%

Dividend = 12% of face value

= $\dfrac{12}{100} \times 100$

= ₹ 12.

Market price = Face value - Discount

= ₹ 100 - ₹ 4

= ₹ 96.

By formula,

Return = $\dfrac{\text{Dividend earned on one share}}{\text{Market Price of one share}} \times 100$

= $\dfrac{12}{96} \times 100$

= 12.5%

Hence, option 3 is the correct option.

Akshay buys 350 shares of ₹ 50 par value of a company. The dividend declared by the company is 14%. If his return percent from the shares is 10%, find the market value of each share.

1. ₹ 55

2. ₹ 60

3. ₹ 65

4. ₹ 70

Answer

Given,

Rate of dividend = 14%

Dividend on ₹ 50 = $\dfrac{14}{100} \times 50$ = ₹ 7.

Given,

Return percent from the shares is 10%.

∴ Interest on ₹ 100 = $\dfrac{10}{100} \times 100$ = ₹ 10.

∴ ₹ 7 will be interest on $\dfrac{100}{10} \times 7$ = ₹ 70.

Hence, Option 4 is the correct option.

Mr. Das invests in ₹ 100, 12% shares of Company A available at ₹ 60 each. Mr. Singh invests in ₹ 50, 16% shares of Company B available at ₹ 40 each. Which of the following statements is true?

1. The rate of return for Mr. Das is 12%.

2. The rate of return for Mr. Singh is 10%.

3. Both Mr. Das and Mr. Singh have the same rate of return of 10%.

4. Both Mr. Das and Mr. Singh have the same rate of return of 20%.

Answer

For Mr. Das,

Face value of each share = ₹ 100

Market value of each share = ₹ 60

Dividend per share = 12% of ₹ 100 = ₹ 12.

Rate of return = $\dfrac{\text{Dividend per share}}{\text{M.V. of each share}} \times 100 = \dfrac{12}{60} \times 100$ = 20%.

For Mr. Singh,

Face value of each share = ₹ 50

Market value of each share = ₹ 40

Dividend per share = 16% of ₹ 50 = ₹ 8.

Rate of return = $\dfrac{\text{Dividend per share}}{\text{M.V. of each share}} \times 100 = \dfrac{8}{40} \times 100$ = 20%.

∴ Both Mr. Das and Mr. Singh have the same rate of return of 20%.

Hence, Option 4 is the correct option.

Assertion (A): Market value of a share always remains the same.

Reason (R): The value of a share printed on the share certificate is called its face value.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Answer

(A) Market value of a share always remains the same.

This is false because market value changes frequently depending on factors like demand, supply, company performance, and market conditions.

So, Assertion (A) is false.

The value printed on a share certificate is called the face value or nominal value.

So, Reason (R) is true.

Hence, Option 4 is correct option.

Assertion (A): Income of a shareholder is directly proportional to the number of shares he buys.

Reason (R): Income of a shareholder

= $\text{Face value} \times \dfrac{ \text{No. of shares} \times \text{Rate of dividend}}{100}$

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Answer

Income of a shareholder is directly proportional to the number of shares he buys. This is true because the more shares one holds, the greater the total dividend received. So, income increases with the number of shares.

So, Assertion (A) is true.

By formula,

$\text{Income} = \text{Face value} \times \text{No. of shares} \times \dfrac{ \text{Rate of dividend}}{100}$

So, Reason (R) is also true.

Both A and R are true, and R is the correct explanation of A.

Hence, Option 1 is the correct option.

Assertion (A): Investing in 12% of the 100 shares at ₹ 150 means, an investment of ₹ 100 gives an annual income of ₹ 12.

Reason (R): Annual income of an investor depends upon the face value of the share.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Answer

Given,

Face value = ₹ 100

Market value = ₹ 150

Dividend rate = 12%

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

$\text{Annual income from one share} = 1 \times \dfrac{12}{100} \times 100 = ₹12$

However, the investment was ₹ 150 (the market price), not ₹ 100.

So, an investment of ₹100 does not give ₹ 12 in income — ₹ 12 is earned on ₹ 150.

∴ Assertion (A) is false.

By formula,

Annual income = No. of shares × Rate of div. × N.V. of 1 share

This means the income does depend on the face value, not the market value.

∴ Reason (R) is true.

Hence, Option 4 is the correct option.

Assertion (A): A man invests ₹ 4,600 in ₹ 100 shares, paying 10% dividend and quoted at 15% premium. His annual dividend from these shares is ₹ 400.

Reason (R): Number of shares held by a person = $\dfrac{\text{Total market value}}{\text{Face value of 1 share}}$

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Answer

Given,

Investment = ₹ 4,600

Rate of Div. = 10%

Face Value = ₹ 100

Premium Rate = 15%

Premium = 15% of 100 = $\dfrac{15}{100} \times 100$ = ₹ 15

Market Value = Face value + Premium = ₹ 100 + ₹ 15 = ₹ 115

By formula,

$\text{Number of shares} = \dfrac{ \text{ Investment }}{ \text{ Market value of each share}}\\[1em] = \dfrac{4600}{115} = 40. \\[1em] \text{Annual dividend} = \text{No. of shares} \times \text{Rate of div.} \times \text{ N.V. of 1 share}\\[1em] = 40 \times \dfrac{10}{100}\times 100 = ₹ 400.$

∴ Assertion (A) is true.

By formula,

$\text{Number of shares} = \dfrac{\text{Total Investment}}{\text{Market Value per share}}$

∴ Reason (R) is false.

Hence, Option 3 is the correct option.

Ankit has the option of investing in company A, where 7%, ₹ 100 shares are available at ₹ 120 or in company B, where 8%, ₹ 1000 shares are available at ₹ 1620.

Assertion (A): Investment in Company A is better than Company B.

Reason (R): The rate of income in Company A is better than in Company B.

1. Both A and R are true, and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true, but R is false.

4. A is false, but R is true.

Answer

In company A,

N.V. = ₹ 100

M.V. = ₹ 120

Dividend = 7% = $\dfrac{7}{100} \times 100$ = ₹ 7

∴ Investment = ₹ 120 and income = ₹ 7.

Income on ₹ 1 = $\dfrac{7}{120}$ = ₹ 0.0583

In company B,

N.V. = ₹ 1000

M.V. = ₹ 1620

Dividend = 8% = $\dfrac{8}{100} \times 1000$ = ₹ 80

∴ Investment = ₹ 1620 and income = ₹ 80.

Income on ₹ 1 = $\dfrac{80}{1620}$ = ₹ 0.0494

Since, rate of income is greater in company A.

∴ Assertion and Reason both are true and Reason is the correct explanation of Assertion.

Hence, Option 1 is the correct explanation.

Answer

Aman has 500, ₹ 100 shares of a company quoted at ₹ 120, paying a 10% dividend. When the share price rises to ₹ 200 each, he sells all his shares. He invests half of the sale proceeds in ₹ 10, 12% shares at ₹ 25, and the remaining sale proceeds in ₹ 400, 9% shares at ₹ 500.

Find his:

(i) sales proceeds

(ii) investment in ₹ 10, 12% shares at ₹ 25

(iii) original income

(iv) change in income

Answer

(i) No. of shares Aman sells = 500

Aman sells the share when they rise to ₹ 200.

Sale proceeds = 500 × ₹ 200 = ₹ 1,00,000.

Hence, sale proceeds = ₹ 1,00,000.

(ii) Given,

Aman invests half of the sale proceeds in ₹ 10, 12% shares at ₹ 25.

∴ Investment = $\dfrac{\text{Sale proceeds}}{2} = \dfrac{100000}{2}$ = ₹ 50,000

Hence, investment in ₹ 10, 12% shares at ₹ 25 = ₹ 50,000.

(iii) By formula,

Income = No. of shares × $\dfrac{\text{Rate of dividend}}{100}$ × Nominal value of share

= 500 × $\dfrac{10}{100}$ × 100

= ₹ 5,000.

Hence, original income = ₹ 5,000.

(iv) Aman invests ₹ 50,000 in each of the new shares.

For 1st share :

N.V. = ₹ 10

Dividend = 12%

M.V. = ₹ 25

No. of shares bought = $\dfrac{50000}{25}$ = 2000.

Income = No. of shares × $\dfrac{\text{Rate of dividend}}{100}$ × Nominal value of share

= 2000 × $\dfrac{12}{100}$ × 10

= ₹ 2,400.

For 2nd share :

N.V. = ₹ 400

Dividend = 9%

M.V. = ₹ 500

No. of shares bought = $\dfrac{50000}{500}$ = 100.

Income = No. of shares × $\dfrac{\text{Rate of dividend}}{100}$ × Nominal value of share

= 100 × $\dfrac{9}{100}$ × 400

= ₹ 3,600.

New income = ₹ 3,600 + ₹ 2,400 = ₹ 6000

Change in income = New income - Original income = ₹ 6,000 - ₹ 5,000 = ₹ 1,000.

Hence, change in income = ₹ 1,000 (increase).