Rishi has ₹1,612 with him. He divided it amongst his sons Shan and Piyush and asked them to invest it at 8% rate of interest per annum, compounded annually. It was seen that Shan and Piyush got the same amount after 19 and 20 years, respectively. How much (in ₹) did Rishi give to Shan?

Correct option is D

Given:

Total money (₹) = ₹1,612

Rate of interest (r) = 8% per annum

Time for Shan (t₁) = 19 years

Time for Piyush (t₂) = 20 years

Amount received by both = Equal

Formula used:
A$$= P \times (1 + \frac{r}{100})^t$$​​

Solution:
Let the amount given to Shan be ₹x. Then, the amount given to Piyush will be ₹(1612 - x).

Using the formula for compound interest:

$$P \times (1 + \frac{r}{100})^{t₁} = P \times (1 + \frac{r}{100})^{t₂} \\ \ \\x \times (1 + \frac{8}{100})^{19} = (1612 - x) \times (1 + \frac{8}{100})^{20} \\ \ \\x \times (1.08)^{19} = (1612 - x) \times (1.08)^{20} \\ \ \\x \times (1.08)^{19} = (1612 - x) \times 1.08 \times (1.08)^{19}\\ \ \\x = (1612 - x) \times 1.08\\ \ \\x = 1612 \times 1.08 - 1.08x\\ \ \\x + 1.08x = 1612 \times 1.08\\ \ \\2.08x = 1740.96\\ \ \\x = \frac{1740.96}{2.08}\\ \ \\x = 837$$​