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 \[8%=\frac{\frac{8}{3}}{\frac{8}{3}+4}\times 20000=\frac{\frac{8}{3}}{\frac{8+12}{3}}\times 20000\] |
\[=\frac{8}{3}\times \frac{3}{20}\times 20000=\text{Rs}\text{. 8000}\] |
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