Question: 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%.
Options:
A) Rs. 8000
B) Rs. 12000
C) Rs. 6000
D) Rs. 10000
Show Answer
Answer:
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{SI\times 100}{P\times 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=Rs\text{. 8000} $