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 Tier II, 2014]

A) Rs. 8000

B) Rs. 12000

C) Rs. 6000

D) Rs. 10000

Correct Answer: A

Solution :

[a] Here, P = Rs. 20000, SI = Rs. 800, T = 1 yr New, average rate at which the amount was invested             \[=\frac{SI\times 100}{P\times T}=\frac{800\times 100}{20000\times 1}=4%\] Now, using the rule of allegation             \[\frac{8}{3}:4\] \[\therefore \]      Sum lent at 8% \[=\frac{\frac{8}{3}\times 20000}{\frac{8}{3}+4}=\frac{\frac{8}{3}}{\frac{8+12}{3}}\times 20000\] \[=\frac{8}{3}\times \frac{3}{20}\times 20000=\text{Rs}.\,\,800\]