Question

On a certain sum, the compound interest in two years amounts to Rs. 2,256. If the rates of interest for successive years are 8% and 10% respectively, find the sum.

• A. Rs. 10000
• B. Rs. 12000
• C. Rs. 14000
• D. Rs. 16000

Answer 1

The correct option is B Rs. 12000

Let the sum be P

Rate of interest=8% ,10%

$A=P(1+\frac{8}{100})(1+\frac{10}{100})\because A=P(1+\frac{r_1}{100})(1+\frac{r_2}{100})$
$A=P\times \frac{108}{100}\times \frac{110}{100}=\frac{297}{250}P$

$C.I.=Rs.2256$
$\Rightarrow \frac{297}{250}P-P=2256[\because C.I.=A-P]$

$\Rightarrow \frac{297P-250P}{250}=2256$

$\Rightarrow P=\frac{2256\times 250}{47}=12000$
$\therefore$ Required sum = Rs. 12000