Question

Two equal sums of money were lent at simple interest at $11$% p.a. for $3\frac{1}{2}$ years and $4\frac{1}{2}$ years respectively. If the difference in interest for two periods was $Rs.412.50$, find the each sum.

• A. $Rs.3250$
• B. $Rs.3500$
• C. $Rs.3750$
• D. $Rs.4250$

Answer 1

The correct option is D $Rs.4250$

Solution:-

Let each sum be $x$.

Given that rate of interest is $11\%$

Now according to the question-

$\frac{x\times 11\times 9}{100\times 2}-\frac{x\times 11\times 7}{100\times 2}=412.5$

$99x-77x=412.5\times 200$

$\Rightarrow 22x=82500$

$\Rightarrow x=\frac{82500}{22}=3750$

Hence the value of each sum is $Rs.3750$.