Question : The simple interest on a certain sum for 3 years at 14% p.a. is INR 4,200 less than the simple interest on the same sum for 5 years at the same rate. Find the sum.
Option 1: INR 16,000
Option 2: INR 10,000
Option 3: INR 15,000
Option 4: INR 12,000
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Correct Answer: INR 15,000
Solution :
Let $P$ be the principal sum.
Rate, $R$ = 14%
Time, $n_1$ = 3 years
Time, $n_2$ = 5 years
Simple interest, SI = $\frac{PnR}{100}$
According to the question,
$\frac{P×5×14}{100}$ – $\frac{P×3×14}{100}$ = 4200
⇒ $\frac{P×2×14}{100}$ = 4200
⇒ $P$ = $\frac{420000}{28}$ = 15,000
Hence, the correct answer is INR 15,000.
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