Question

A man invests $\frac{1}{3}$ of his capital at $7\%$ p.a., $\frac{1}{4}$ at $8\%$ p.a. and the remainder at $10\%$ p.a. If his annual income is Rs. $561$, the capital is

• A. Rs, $5400$
• B. Rs. $6000$
• C. Rs. $6600$
• D. Rs. $7200$

Answer 1

The correct option is C Rs. $6600$

Let the capital be Rs. $x$

Then according to the question, we have

$\frac{\frac{x}{3}\times 7\times 1}{100}+\frac{\frac{x}{4}\times 8\times 1}{100}+\frac{\left(\begin{array}{c}x-\frac{x}{3}-\frac{x}{4}\end{array}\right)\times 10\times 1}{100}=561$

$\Rightarrow \frac{7x}{300}+\frac{8x}{400}+\frac{50x}{1200}=561$

$\Rightarrow \frac{28x+24x+50x}{1200}=561$

$\Rightarrow \frac{102x}{1200}=561$

$\Rightarrow x=\frac{561\times 1200}{102}=Rs.6600$.