Mark (✓) against the correct answer:
If the simple interest on a sum of money at 10% per annum for 3 years is Rs 1500, then the compound interest on the same sum at the same rate for the same period is
(a) Rs 1655
(b) Rs 1155
(c) Rs 1555
(d) Rs 1855
(a) Rs 1655
Here, SI $=\frac{P \times R \times T}{100}$
$\Rightarrow$ Rs. $1500=\frac{P \times 10 \times 3}{100}$
$\Rightarrow P=\frac{1500 \times 100}{10 \times 3}=$ Rs. 5000
Now, $A=P \times\left(1+\frac{R}{100}\right)^{n}$
$=$ Rs. $5000 \times\left(1+\frac{10}{100}\right)^{3}$
$=$ Rs. $5000 \times\left(\frac{110}{100}\right)^{3}$
$=$ Rs. $5000 \times\left(\frac{11}{10}\right) \times\left(\frac{11}{10}\right) \times\left(\frac{11}{10}\right)$
$=$ Rs. $(5 \times 11 \times 11 \times 11)$
$=$ Rs. 6655
$\therefore$ CI $=A-P=$ Rs $(6655-5000)=$ Rs 1655