Question

Divide Rs.15,600 into two parts such that the simple interest on one at 5 percent for 5 years may be equal to that on the other at $4\frac{1}{2}$ per cent for 6 years.

• A. Rs.$7,400$ and Rs.$8,300$
• B. Rs.$7,700$ and Rs.$8,500$
• C. Rs.$8,700$ and Rs.$7,000$
• D. Rs.$8,100$ and Rs.$7,500$

Answer 1

The correct option is D Rs.$8,100$ and Rs.$7,500$

Let the parts be $RsA;Rs15,600-A$

Simple Interest $I=\frac{PNR}{100}$

For the first situation, Given,

$P=RsA$

$N=5years$

$R=5$ %

So, $=>I=\frac{PNR}{100}$

$=>I_1=\frac{A\times 5\times 5}{100}$

$=>I_1=\frac{25A}{100}$
For the second situation, Given,

$P=Rs15,600-A$

$N=6years$

$R=\frac{9}{2}$ %

So, $=>I=\frac{PNR}{100}$

$=>I_2=\frac{(15,600-A)\times 6\times \frac{9}{2}}{100}$

$=>I_2=\frac{(15,600-A)\times 27}{100}$

Given, $I_1=I_2$

$=>\frac{25A}{100}=\frac{(15,600-A)\times 27}{100}$

$25A=(15,600-A)\times 27$

$25A=421200-27A$

$=>52A=421200$

$=>A=Rs8,100$

And other part $=Rs15,600-Rs8,100=Rs7,500$