Question

A sum of Rs. $10000$ is lent partly at $8\%$ and remaining at $10\%$ per annum. If the yearly interest on the average is $9.2\%$, what are the two parts?

• A. Rs. $4000$ and Rs. $6000$
• B. Rs. $3000$ and Rs. $7000$
• C. Rs. $2000$ and Rs. $8000$
• D. Rs.$1000$ and Rs. $8000$

Answer 1

The correct option is A Rs. $4000$ and Rs. $6000$

Let the sum lent at $8\%p.a.$ be Rs. $x$.

Then, the sum lent at $10\%p.a.$ is Rs. $(10000-x)$

Then according to the question, we have
$\therefore \frac{x\times 8\times 1}{100}+\frac{(10000-x)\times 10\times 1}{100}=\frac{9.20\times 10000}{100}$

$\Rightarrow \frac{8x}{100}+1000-\frac{10x}{100}=920$

$\Rightarrow \frac{8x}{100}-\frac{10x}{100}=920-1000$
$\Rightarrow -\frac{2x}{100}=-80$

$\Rightarrow 2x=8000$

$\Rightarrow x=4000$
$\therefore$ The two parts are Rs. $4000$ and Rs. $6000$.