Question : Two equal sums are lent at 8% and 4% simple interest p.a, respectively at the same time. The first sum is received 2 years earlier than the other and the amount received in each case is INR 14,500. Each sum is:
Option 1: INR 12,800
Option 2: INR 12,500
Option 3: INR 13,200
Option 4: INR 12,000
Correct Answer: INR 12,500
Solution :
$R_1 = 8$%
$R_2 = 4$%
Let $P$ be the principal sum in both cases and $n$ be the time for the first amount.
⇒ Time for second amount = $n+2$
Since both amounts are equal, simple interest will also be equal.
⇒ $\frac{P_1n_1R_1}{100} = \frac{P_2n_2R_2}{100}$
⇒ $\frac{P×n×8}{100} = \frac{P×(n+2)×4}{100}$
⇒ $8n = 4(n+2)$
⇒ $8n = 4n +8$
⇒ $n = 2$
Total amount = 14500
So, $P + \frac{Pn_1R_1}{100} = 14500$
⇒ $P(1+\frac{2×8}{100}) = 14500$
⇒ $P = \frac{1450000}{116} = 12,500$
Hence, the correct answer is INR 12,500.
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