Question

If a certain sum of money amounts to $Rs.1760$ in two years and $Rs.2000$ in $5$ years at simple interest, then the sum is:

• A. $Rs.1960$
• B. $Rs.1590$
• C. $Rs.1600$
• D. None of these

Answer 1

The correct option is C $Rs.1600$

Given:

A certain sum of money amounts to $Rs.1760$ in $2$ years and $Rs.2000$ in $5$ years at simple interest.

To find: Principal Amount, $P$

We know that,

Simple Interest, $S.I.=\frac{P\times R\times N}{100}$

where,

$P$ is principal amount, $R$ is rate of interest per annum and $N$ is number of years.
$SI$ on amount $P$ for $2$ years at rate $R$

${SI}_2=\frac{2PR}{100}$

Total amount after $2$ years is $Rs.1760$ (given),

Amount, $Rs.1760=P+{SI}_2=P+\frac{2PR}{100}$ ....(1)

$SI$ on amount $P$ for $5$ years at rate $R$

${SI}_5=\frac{5PR}{100}$

Total amount after $5$ years is $Rs.2000$ (given),

Amount, $Rs.2000=P+{SI}_5=P+\frac{5PR}{100}$ ....(2)

Subtracting (1) from (2), we get

$\frac{3PR}{100}=Rs.240$

$\Rightarrow PR=Rs.8000$

Substitute the value of $PR$ in (1), we get

$1760=P+\frac{2\times 8000}{100}$

$P=Rs.1600$

Hence, option C.