Question : If the amount obtained by A by investing INR 9,100 for three years at a rate of 10% p.a. on simple interest is equal to the amount obtained by B by investing a certain sum of money for five years at a rate of 8% p.a. on simple interest, then 90% of the sum invested by B (in INR) is:
Option 1: 8,450
Option 2: 7,800
Option 3: 8,540
Option 4: 7,605
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Correct Answer: 7,605
Solution : Principal of A = INR 9,100 Rate of A = 10% Time of A = 3 years Rate of B = 8% Time of B = 5 years According to the question Simple interest, SI = $\frac{\text{Principal × Rate × Time}}{100}=\frac{(9100 × 10 × 3)}{100}=$ INR 2,730 Amount = Principal + Simple interest = INR (9100 + 2730) = INR 11,830 Let the Principal of B be $P$ Simple interest $=\frac{(P × 8 × 5)}{100}=\frac{2P}{5}$ Amount = Principal + SI $=(P + \frac{2P}{5})=\frac{7P}{5}$ According to the question, $\frac{7P}{5}$ = 11,830 ⇒ 7P = 59,150 ⇒ P = INR 8,450 90% of the sum invested by B = $(\frac{90}{100}\times 8450)=$ INR 7,605 Hence, the correct answer is INR 7,605.
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