Question

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. If his total annual income from both the investments is Rs 2000, then his total investment is ____

• A. Rs 16500, 200
• B. Rs 15,000, 200
• C. Rs 14, 000, 100
• D. Rs 12, 000, 180

Answer 1

The correct option is A

Rs 16500, 200

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

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

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

No. of shares bought = $\frac{\text{money invested}}{\text{Market value of shares}}$
= $\frac{2x}{5\times 60}$
= $\frac{x}{150}$
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 $=\frac{3x}{55}+\frac{x}{15}$
$\Rightarrow 2000=\frac{3x}{55}+\frac{x}{15}$
$\Rightarrow 2000=\frac{9x+11x}{5\times 11\times 3}$
$\Rightarrow 2000=\frac{20x}{5\times 11\times 3}$
$\Rightarrow x=₹16500$