A man invests some money in his shares. He invests $60 %$ of his money at $10 %$ . Rs 100 shares at Rs 110 and the rest in $20 %$ . Rs 50 shares at Rs 60. Find his total investment if his total annual income from both the investments is Rs 2000.

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Solution

Given, Face value of a share of first type = ₹ 100
Face value of a share of $2^{n d}$ type = ₹ 50
Let the investment be ₹ x.

Shares Type 1:
Investment in first kind of shares = 60% of x = $\frac{60 x}{100} = ₹ \frac{3}{5} x$
No. of shares bought = $\frac{money invested}{Market value of shares}$
= $\frac{3 x}{5} \times \frac{1}{110}$
= $\frac{3 x}{550}$
Dividend earned = Rate of Dividend $\times$ No. of shares $\times$ Nominal value of each share
$= \frac{10}{100} \times \frac{3 x}{550} \times 100$
=₹ $\frac{3 x}{55}$

Shares Type 2:
Investment in second kind of shares = 40% of x
= $\frac{40 x}{100}$
= ₹ $\frac{2}{5} x$

No. of shares bought = $\frac{money invested}{Market value of shares}$
= $\frac{2 x}{5 \times 60}$
= $\frac{x}{150}$
Dividend earned = Rate of Dividend $\times$ No. of shares $\times$ Nominal value of each share
= $\frac{20}{100} \times \frac{x}{150} \times 50$
=₹ $\frac{x}{15}$

Total dividend Earned $= \frac{3 x}{55} + \frac{x}{15}$
$\Rightarrow 2000 = \frac{3 x}{55} + \frac{x}{15}$
$\Rightarrow 2000 = \frac{9 x + 11 x}{5 \times 11 \times 3}$
$\Rightarrow 2000 = \frac{20 x}{5 \times 11 \times 3}$
$\Rightarrow x = ₹ 16500$

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