Pravin has Rs. 1612 with him. He divided it amongst his sons Rishi and Shan and asked them to invest it at 8% rate of interest compounded annually. It was seen that Rishi and Shan got same amount after 17 and 18 years respectively. How much (in Rs. ) did Pravin give to Rishi?

Correct option is D

Given:

Total amount Pravin has: ₹1612

Rishi invests for 17 years, and Shan invests for 18 years at a 8% annual compound interest rate.

Formula Used:

The formula for compound interest is:

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

Where:

A is the amount after t years,

P is the principal (initial amount),

r is the rate of interest 

t is the time in years.

Solution:

Let the amount given to Rishi be$$P_1$$and the amount given to Shan be$$P_2$$​. Therefore, 

​$$P_1 + P_2 = 1612$$​​

For Rishi 

​$$A_1 = P_1 \left( 1 + \frac{8}{100} \right)^{17} = P_1 \times 1.08^{17}$$​​

For Shan

​$$A_2 = P_2 \left( 1 + \frac{8}{100} \right)^{18} = P_2 \times 1.08^{18}$$​​

Given that $$A_1 = A_2:$$​​

​$$P_1 \times 1.08^{17} = P_2 \times 1.08^{18}$$​​

​$$P_1 = P_2 \times \frac{1.08^{18}}{1.08^{17}} = P_2 \times 1.08$$​​

​$$P_1 = 1.08 \times P_2$$​​

Substituting $$P_1 = 1.08 \times P_2$$​ into $$P_1 + P_2 = 1612:$$​​

​$$1.08 \times P_2 + P_2 = 1612$$​​

​$$P_2 = \frac{1612}{2.08} = 775$$​​

Now,

​$$P_1 = 1.08 \times 775 = 837$$​​

Thus, Pravin gave ₹837 to Rishi