Shares & Dividends — Assertion-Reason Type Questions

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