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Question:

To start a new enterprise, Mr. Yogesh has borrowed a total of Rs. 60,000 from two money lenders with the interest being compounded annually, to be repaid at the end of two years. Mr. Yogesh repaid Rs.38, 800 more to the first money lender compared to the second money lender at the end of two years. The first money lender charged an interest rate, which was 10% more than what was charged by the second money lender. If Mr. Yogesh had instead borrowed Rs. 30,000 from each at their respective initial rates for two years, he would have paid Rs.7,500 more to the first money lender compared to the second. Then money borrowed by Mr. Yogesh from first money lender is?

Explanation:

Let the rate of second lender be y%, then rate of first lender is (y + 10)%.

When they lend equal amounts

30000 ${(1 + \frac{y + 10}{100})}^{2}$ - 30000 ${(1 + \frac{y}{100})}^{2}$ = 7500

∴ ${(\frac{110 + y}{100})}^{2}$ - ${(\frac{100 + y}{100})}^{2}$ = $\frac{1}{4}$

∴ 110² - 100² + 220y - 200y = 2500

y = 20%

Now we evaluate options and find that option 3 satisfies conditions.

40000 ${(1 + \frac{30}{100})}^{2}$ - 20000 ${(1 + \frac{20}{100})}^{2}$ = 38800

Hence, option (c).

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