a sum of Rs. 34533 is divided between rohit and rajesh, 18 years and 21 years old be invested at 5% per annum compound interest, both will receive equal at the age of 30 years. find the shares of each out of Rs. 34,522

Answer :
We have total money = Rs. 34,522
Let Rohit have share of money = Rs . x 
And
Rajesh have share of money = Rs . 34,522 - x 

Rate = 5%
Time for Rohit = 30 - 18 = 12 years
Time for Rajesh = 30 - 21 = 9 years
And they recieve equal money at that time So,

Rohit' s money = Rajesh money
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 share money = 16000 rs
And 
Rajesh share = 34,522 - 16000 = ​18522 rs                          ( Ans )