Question

The simple interest on a certain sum for 8 years at 12% per annum is ₹3,120 more than the simple interest on the same sum for 5 years at 14 % per annum. Find the sum.

Answer 1

Given, $I_1-I_2$ = ₹3,120
$T_1$ = 8 yrs, $R_1$ = 12 %
$T_2$ = 5 yrs, $R_2$ = 14 %
and $P_1=P_2=P$
According to the question,
$I_1-I_2$ = ₹3,120
$\Rightarrow \frac{P_1\times R_1\times T_1}{100}-\frac{P_2\times R_2\times T_2}{100}=3,120\Rightarrow \frac{P\times 12\times 8}{100}-\frac{P\times 14\times 5}{100}=3,120\Rightarrow \frac{P}{100}[12\times 8-14\times 5]=3,120\Rightarrow P[96-70]=3,120\times 100\Rightarrow 26P=3,12,000\Rightarrow P=\frac{3,12,000}{26}$
$P$ = ₹12,000
Hence, the sum is ₹12,000.