Question

A man invested one-third of his capital at $7\%$, one-fourth at $8\%$ and the rest at $10\%$ simple interest, respectively. If his annual income is $₹561$. What will be the capital?

Answer 1

Let the capital be $₹x$.

According to the given conditions, we have

$$\begin{gathered} (\frac{x}{3}\times \frac{7}{100}\times 1)+(\frac{x}{4}\times \frac{8}{100}\times 1)+(\frac{5x}{12}\times \frac{10}{100}\times 1)=561 \\ \Rightarrow \frac{7x}{300}+\frac{x}{50}+\frac{x}{24}=561 \\ \Rightarrow \frac{14x+12x+25x}{600}=561\times 600 \\ \Rightarrow 51x=336600 \\ \Rightarrow x=\frac{336600}{51} \\ \Rightarrow x=6600 \end{gathered}$$

Hence, the capital will be worth $\mathbf{₹}\mathbf{}\mathbf{6600}$.