Mr. Gupta has a choice to invest in ten-rupee shares of two firms at ₹ 13 or at ₹ 16. If the first firm pays 5% dividend and the second firm pays 6% dividend per annum, find :

(i) which firm is paying better.

(ii) if Mr. Gupta invests equally in both the firms and difference between the returns from them is ₹ 30, find how much, in all, does he invest?

(i) First firm :

Nominal value of 1 share = ₹ 10

M.V. = ₹ 13

Dividend = 5%

Dividend = 1 × $\dfrac{5}{100} \times 10$ = 0.50

Income% = $\dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{0.5}{13} \times 100$ = 3.846%

Second firm :

Nominal value of 1 share = ₹ 10

M.V. = ₹ 16

Dividend = 6%

Dividend = 1 × $\dfrac{6}{100} \times 10$ = 0.60

Income% = $\dfrac{\text{Income}}{\text{Investment}} \times 100 = \dfrac{0.6}{16} \times 100$ = 3.75%

Hence, first firm pays better.

(ii) Let investment on both firms be ₹ x each.

In first case :

M.V. = ₹ 13

No. of shares = $\dfrac{x}{13}$

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

$= \dfrac{x}{13} \times \dfrac{5}{100} \times 10 \\[1em] = \dfrac{x}{26}.$

In second case :

M.V. = ₹ 16

No. of shares = $\dfrac{x}{16}$

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

$= \dfrac{x}{16} \times \dfrac{6}{100} \times 10 \\[1em] = \dfrac{3x}{80}.$

Given, difference between returns = ₹ 30

$\Rightarrow \dfrac{x}{26} - \dfrac{3x}{80} = 30 \\[1em] \Rightarrow \dfrac{40x - 39x}{1040} = 30 \\[1em] \Rightarrow \dfrac{x}{1040} = 30 \\[1em] \Rightarrow x = 30 \times 1040 = 31,200.$

Total investment = x + x = 2x = 2 x 31200 = ₹ 62,400.

Hence, total investment = ₹ 62,400.