# A sum of 34522 is divided between Rohit and Rajesh, 18 years and 21 years old respectively in such a way that if their shares be invested at 5% p.a. Compound Interest, both will receive equal money at the age of 30 years. Find the shares of each.

Answer :

We have total money = Rs. 34,522

Let Rohit has share of money = Rs .

*x*

And

Rajesh has share of money = Rs . 34,522 -

*x*

Rate = 5%

Time period for Rohit = 30 - 18 = 12 years

Time period for Rajesh = 30 - 21 = 9 years

And they receive equal money at that time So,

Compound interest on

*x*for 12 years = Compound interest on ( 34,522 -

*x*) for 9 years As:

$x{\left[1+\frac{5}{100}\right]}^{12}$ = ( 34522 -

*x*) ${\left[1+\frac{5}{100}\right]}^{9}$

Now we divide by ${\left[1+\frac{5}{100}\right]}^{9}$ on both hand side , we get

*x ${\left[1+\frac{5}{100}\right]}^{3}$ =*34,522 -

*x*

*x*( 1.05 )

^{3}= 34,522 -

*x*

1.157625

*x*+

*x*= 34,522

*x*= $\frac{34,522}{2.157625}$

*x*= 16000

So

Rohit's share of money = 16000 rs

And

Rajesh's share of money = 34,522 - 16000 = 18522 rs

Regards

**
**