Gagan invested 80% of his savings in 10% ₹ 100 shares at 20% premium and the rest of his savings in 20% ₹ 50 shares at 20% discount. If his incomes from these shares is ₹ 5,600, calculate :

(i) his investment in shares on the whole

(ii) the number of shares of first kind that he bought

(iii) percentage return, on the shares bought, on the whole.

(i) Let total savings be ₹ x.

For 1st part :

N.V. of each share = ₹ 100

M.V. of each share = ₹ 100 + $\dfrac{20}{100} \times 100$ = ₹ 120.

Investment on these shares = $\dfrac{80}{100} \times x$ = 0.8x

No. of shares bought = $\dfrac{0.8x}{120}$

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

= $\dfrac{0.8x}{120} \times \dfrac{10}{100} \times 100 = \dfrac{0.8x}{12}$.

For 2nd part :

N.V. of each share = ₹ 50

M.V. of each share = ₹ 50 - $\dfrac{20}{100} \times 50$ = ₹ 50 - ₹ 10 = ₹ 40.

Investment on these shares = $\dfrac{20}{100} \times x$ = 0.2x

No. of shares bought = $\dfrac{0.2x}{40}$

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

= $\dfrac{0.2x}{40} \times \dfrac{20}{100} \times 50 = \dfrac{0.2x}{4}$.

Given, income (dividend) from both shares = ₹ 5,600

$\therefore \dfrac{0.8x}{12} + \dfrac{0.2x}{4} = 5600 \\[1em] \Rightarrow \dfrac{0.8x + 0.6x}{12} = 5600 \\[1em] \Rightarrow \dfrac{1.4x}{12} = 5600 \\[1em] \Rightarrow x = \dfrac{5600 \times 12}{1.4} \\[1em] \Rightarrow x = 48,000.$

Hence, total investment = ₹ 48,000.

(ii) So, the number of shares of first kind = $\dfrac{0.8x}{120} = \dfrac{0.8 \times 48000}{120} = 320.$

Hence, no. of shares of first kind = 320.

(iii) Total dividend (return) =

$= \dfrac{0.8x}{12} + \dfrac{0.2x}{4} \\[1em] = \dfrac{0.8 \times 48000}{12} + \dfrac{0.2 \times 48000}{4} \\[1em] = 3200 + 2400 \\[1em] = 5600$

Percentage return = $\dfrac{\text{Return}}{\text{Investment}} \times 100 = \dfrac{5600}{48000} \times 100 = 11\dfrac{2}{3}$%

Hence, percentage return = $11\dfrac{2}{3}$%.