question_answer

Prakash lends a part of Rs. 20000 at 8% simple interest and remaining at \[\frac{4}{3}%\]simple interest. His total income after a year was Rs. 800. Find the sum lent at 8%.                                      [SSC (CGL) Mains 2014]

A) Rs. 8000           

B) Rs. 12000

C) Rs. 6000                       

D) Rs. 10000

Correct Answer: A

Solution :

Here, P = Rs. 20000, SI = Rs. 800 and T = 1 yr

Now, average rate at which the amount was invested

\[\frac{\text{SI}\times 100}{\text{P}\times \text{T}}=\frac{800\times 100}{20000\times 1}=4%\]

From alligation rule,

\[\therefore \]Sum lent at \[8%=\frac{\frac{8}{3}}{\frac{8}{3}+4}\times 20000=\frac{\frac{8}{3}}{\frac{8+12}{3}}\times 20000\]

\[=\frac{8}{3}\times \frac{3}{20}\times 20000=\text{Rs}\text{. 8000}\]