Discussion
The simple interest on a certain sum for 10 years at 9.5% p.a. is ₹ 2,832 less than the amount of the same sum for \(3\frac{1}{2}\) years at 7 % p.a., simple interest. The sum (in ₹) is:
Answer: C
The sum is ₹ 9,600. Let the sum be \(P\). Simple interest for 10 years at 9.5% is \(0.95P\). The amount for \(3\frac{1}{2}\) years at 7% simple interest is \[ P\left(1 + \frac{7\times 3.5}{100}\right) = 1.245P \] The interest is less than that amount by 2,832: \[ 1.245P - 0.95P = 0.295P = 2832 \] \[ P = \frac{2832}{0.295} = 9600 \] Check: 0.95 × 9600 = 9120 and 1.245 × 9600 = 11952, which differ by 2832. The other sums do not give that difference.
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