Question

Shan has INR 1612 with him. He divided it amongst his sons Piyush and Manoj and asked them to invest it at 8% rate of interest compounded annually. It was seen that Piyush and Manoj got same amount after 12 and 13 years respectively. How much (in INR) did Shan give to Piyush?

• A. 687
• B. 875
• C. 837
• D. 775

Answer 1

Answer:

C. 837

Let the amount given to Piyush = ₹P
Then amount given to Manoj = ₹(1612 − P)

Given:

• Rate of interest = 8% p.a. (compound annually)

• Time for Piyush = 12 years

• Time for Manoj = 13 years

• Final amounts are equal

$P(1.08)^{12} = (1612 - P)(1.08)^{13}$
Divide both sides by $((1.08)^{12}):$

$P = (1612 - P)(1.08)$
$P = 1.08 \times 1612 - 1.08P$
$P + 1.08P = 1740.96$
$2.08P = 1740.96$
$P = \frac{1740.96}{2.08} = 837$