Question

Mark (✓) against the correct answer
A sum amounts to Rs $3626$ in $219$ days at $6\%$ per annum simple interest. The sum is
(a) Rs $3000$
(b) Rs $3200$
(c) Rs $3500$
(d) Rs $3600$

Answer 1

The correct option is (c) ($3500$)
Given, total amount is $A=Rs3626,R=6$, $T=219$ $\text{days}=\frac{219}{365}\text{years}$
Let principal(sum) be$=x$
Since simple interest is Rs $S.I.=\frac{P\times R\times T}{100}$
$=\frac{x\times 6\times 219}{100\times 365}$
$=\frac{1314x}{36500}$
Since, $A=P+S.I.$
$A=x+\frac{1314x}{36500}$
$=\frac{36500x+1314x}{36500}$
Thus, $A=\frac{37814x}{36500}$
But the amount is $A=$Rs $3626$.
$\Rightarrow \frac{37814x}{36500}=3626$
$\Rightarrow x=3626\times \frac{36500}{37814}$
$=\frac{132349000}{37814}$
$\therefore x=Rs.3500$
Hence, the required sum is Rs $3500$
So, the correct option is C.