Question

A certain sum of money $Q$ was deposited for $5$ years and $4$ months at $4.5\%$ simple interest and amounted to $Rs248.$ Then the value of $Q$ is

• A. $Rs200$
• B. $Rs210$
• C. $Rs220$
• D. $Rs240$

Answer 1

The correct option is A $Rs200$

When the principal is $P$, the rate of interest is $R$ per annum and the time period is $T$ years then the simple interest is given by,

$SI=\frac{P\times T\times R}{100}$

Given:

$P=Q$

$R=4.5\%$

$T=5$ years $4$ months

$=5\frac{4}{12}$

$=5\frac{1}{3}$

$=\frac{16}{3}$

So,

$SI=\frac{Q\times 16\times 4.5}{100\times 3}$

$=\frac{24Q}{100}$

Principal $+$ Interest $=$ Amount
$\Rightarrow Q+\frac{24Q}{100}=248$
$\Rightarrow 100Q+24Q=24800$

$\Rightarrow 124Q=24800$
$\Rightarrow Q=Rs200$