Question

A sum of Rs. 10,000 is lent partly at 8% and remaining at 10% per annum. If the yearly interest on the average is 9.2%, the two parts are ?

• A. Rs. 4000 , Rs. 6000
• B. Rs. 4500 , Rs. 5500
• C. Rs. 5000 , Rs. 5000
• D. Rs. 5500 , Rs. 4500

Answer 1

Answer: (A)

Rs. 4000 , Rs. 6000

Let the sum lent at $8\%$ is $x$,

then sum lent at $10\%$ is $(10000-x)$

$=x\times \frac{8}{100}\times 1+(10000-x)\times \frac{10}{100}\times 1$

$=\frac{8x}{100}+\frac{10(10000-x)}{100}$

$=\frac{8x+100000-10x}{100}=920$(given) since $9.2\%=9.2\times 100=920$

$\Rightarrow \frac{100000-2x}{100}=920$

$\Rightarrow 100000-2x=92000$

$\Rightarrow 2x=100000-92000=8000$

$\Rightarrow x=\frac{8000}{2}=4000$

$\therefore$ Amount lent at $8\%=$Rs$4000$

and Amount lent at $10\%=$Rs$(10000-4000)=$Rs$6000$