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

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  for 12 years = Compound interest on ( 34,522 - ) for 9 years As:

x 1  + 510012  = ( 34522 -  1  + 51009

Now we divide by  1  + 51009 on both hand side , we get

 1  + 51003 = 34,522 - 

( 1.05 )3 = 34,522 - 
1.157625= 34,522

34,5222.157625

= 16000  
So
Rohit's share of money = 16000 rs
And 
Rajesh's share of money = 34,522 - 16000 = ‚Äč18522 rs                          


Regards
 

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