Ashish has two grandsons Ketan and Mahesh. 15 year old Ketan gets some money from Ashish’s wealth and 16 year old Mahesh gets rest of the money. But Ketan and Mahesh will get money only when they turn 23 years old. Till then the money is in a bank getting interest at rate 4% compounded annually. When both turn 23, they receive the same amount. How much had Ashish given Mahesh (in Rs. ) initially, if total money with Ashish was Rs. 25500?

Correct option is D

Given:

The total money with Ashish = Rs. 25500

Ketan is 15 years old and Mahesh is 16 years old.

Both will receive the money at the age of 23, i.e., in 8 years for Ketan and 7 years for Mahesh.

The interest rate is 4% compounded annually.

Ketan and Mahesh will receive the same amount when they turn 23.

We need to find how much Ashish had given Mahesh initially.

Concept Used:

The formula for compound interest is:

​$$A = P \left(1 + \frac{r}{100}\right)^t$$​​

where:

A is the final amount,

P is the principal,

r is the interest rate,

t is the time period.

Solution:

Let: 

The amount given to Ketan initially be  X,

The amount given to Mahesh initially be Y,

Since they receive the same amount:

​$$X \left(1 + \frac{4}{100}\right)^8 = Y \left(1 + \frac{4}{100}\right)^7 \\ \ \\X \times (1.04)^8 = Y \times (1.04)^7\\ \ \\\frac{X}{Y} = \frac{(1.04)^7}{(1.04)^8} \\ \ \\ \frac{X}{Y} = \frac{100}{104} \\ \ \\ \frac{X}{Y} = \frac{25}{26}$$​​

Now, X = 25P , Y = 26P 

Total amount = 25500

X + Y = 25500 

25P + 26P = 25500 

51P = 25500 

P = $$\frac{25500}{51}$$​ = 500 

Mahesh amount = 26 $$\times$$​ 500 = 13000

Thus, the amount Ashish had given Mahesh initially is Rs. 13000.