Question : Prakash lends a part of Rs. 20,000 at 8% simple interest and the remaining at $\frac{4}{3}\%$ simple interest. His total income after a year was Rs. 800. Find the sum lent at 8%.
Option 1: Rs. 8,000
Option 2: Rs. 12,000
Option 3: Rs. 6,000
Option 4: Rs. 10,000
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Correct Answer: Rs. 8,000
Solution : The total income from the two parts of the sum after a year is equal to Rs. 800. Let the sum lent at 8% as $x$. The remaining sum, which is lent at $\frac{4}{3}\%$, is $(20000 - x)$. Use: Simple Interest = $\frac{\text{Principal × Rate × Time}}{100}$ $⇒\frac{8}{100}x + \frac{4}{300}(20000 - x) = 800$ $⇒8x+\frac{80000}{3}-\frac{4}{3}x=80000$ $⇒8x-\frac{4}{3}x=\frac{160000}{3}$ $⇒\frac{20}{3}x=\frac{160000}{3}$ $⇒ x= 8000$ Hence, the correct answer is Rs. $8000$.
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