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.

Dear student,

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 
1.157625x + 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