Rupesh has two grandsons Mandar and Ketan. 13 year old Mandar gets some money from Rupesh’s wealth and 14 year old Ketan gets rest of the money. But Mandar and Ketan will get money only when they turn 23 years old. Till then the money is in a bank getting interest at rate 5% compounded annually. When both turn 23, they receive the same amount. How much had Rupesh given Ketan (in Rs. ) initially, if total money with Rupesh was Rs. 24600?

Correct option is C

Given:

Mandar’s current age = 13

Ketan’s current age = 14

Both will get the money when they turn 23:

Mandar's money will be invested for 10 years

Ketan's money will be invested for 9 years

Interest rate = 5% compounded annually

Total amount = Rs. 24600

Both will receive the same final amount

Formula Used:

Compound interest formula:

Final Amount = $$\text{Principal} \times \left(1 + \frac {r}{100}\right)^t$$​​

Solution:

Let:

Mandar’s share = x  and Ketan’s share =  y

So, 

​$$x\times \left(1+\frac{5}{100}\right)^{10} = y\times \left(1+\frac{5}{100}\right)^{9} \\ \ \\\implies \frac{x}{y} = \frac{100}{105} =\frac{20}{21}$$​​

So, Let x = 20P , and y = 21P  

x + y  = 24600

20P + 21P = 24600

41P = 24600

P =$$\frac{24600}{41}$$​ = 600

So,
Ketan’s initial share = y = 21P = 21× 600 = Rs. 12600