Question

A sum amounts to Rs. $3605$ in $219$ days at $5\%$ per annum. The sum is
(a) Rs.$3250$
(b) Rs.$3500$
(c) Rs.$3400$
(d) Rs.$3550$

Answer 1

The correct answer is (b) Rs.$3500$
Given Amount $=Rs.3605$
Time $=219$ days $=\frac{219}{365}$ year
Rate$=5\%$ per annum.
Since, Amount $=\text{Sum}+\frac{\text{Sum}\times \text{Rate}\times \text{Time}}{100}$
Which implies, Amount $=\text{sum}(1+\frac{\text{Rate}\times \text{Time}}{100})$
$\Rightarrow 3605=\text{sum}(1+\frac{\frac{219}{365}\times 5}{100})$
$\Rightarrow 3605=\text{sum}(1+\frac{3}{100})$
$\Rightarrow 3605=\text{sum}\times \frac{103}{100}$
$\Rightarrow \text{sum}=3605\times \frac{100}{103}$
$\therefore \text{sum}=Rs.3500$