Veer has Rs. 1224 with him. He divided it amongst his sons Nitin and Pravin and asked them to invest it at 4% rate of interest compounded annually. It was seen that Nitin and Pravin got same amount after 19 and 20 years respectively. How much (in Rs. ) did Veer give to Pravin?

Correct option is C

Given:

Total amount = Rs. 1224

Nitin and Pravin invest their shares at 4% compound interest.

Nitin's investment is for 19 years, and Pravin's investment is for 20 years.

Nitin and Pravin receive the same amount after their respective investment periods.

Formula Used:

Compound interest formula:

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

where, A is the amount after time t, P is the principal amount, R is the rate of interest, and t is the time in years.

Solution:

The principal amounts for Nitin and Pravin are denoted as N and P

the amounts after 19 and 20 years for Nitin and Pravin are equal:

​$$N\left(1 + \frac{4}{100}\right)^{19} = P\left(1 + \frac{4}{100}\right)^{19} \\ \ \\N(1.04)^{19} = P(1.04)^{20} \\ \ \\\frac{N}{P} = \frac{104}{100} = \frac{26}{25}$$​​

Let N = 26 unit, P = 25 unit

So, 

N + P = 1224

(26 + 25 ) unit = 1224 

51 unit = 1224 

1 unit = $$\frac{1224}{51}$$​​

Principle for Pravin =$$\frac{1224}{51} \times 25$$​ = 600 

Thus, Veer gave Rs. 600 to Pravin