Pravin has Rs. 1224 with him. He divided it amongst his sons Rishi and Shan and asked them to invest it at 4% rate of interest compounded annually. It was seen that Rishi and Shan got same amount after 15 and 16 years respectively. How much (in Rs. ) did Pravin give to Shan?

Correct option is A

Given:

Total amount = Rs. 1224

Rishi's amount after 15 years = Shan's amount after 16 years

Rate of interest = 4% p.a. compounded annually

Formula Used:

Amount = Principal × $$\left(1 + \frac{r}{100}\right)^n$$​​

Solution:

Let Rishi receive P₁ and Shan receive P₂ 

Now, 

​$$P_1 \times\left(1 +\frac{4}{100}\right)^{15} = P_2 \times \left(1+\frac{4}{100}\right)^{16} \\ \ \\P_1 \times (1.04)^{15} = P_2 \times (1.04)^{16} \\ \ \\P_1 = 1.04 \times P_2$$​​

Also,

​$$P_1 + P_2 = 1224$$​​

Substitute $$P_1 = 1.04 \times P_2$$​ into the total amount equation:

​$$1.04 \times P_2 + P_2 = 1224 \\ \ \\2.04 \times P_2 = 1224 \\ \ \\P_2 = \frac{1224}{2.04} = 600$$​​

Thus,  Rs 600 was given to Shan