Question

Nitin has INR 1617 with him. He divided it amongst his sons Pravin and Rishi and asked them to invest it at 10% rate of interest compounded annually. It was seen that Pravin and Rishi got same amount after 17 and 18 years respectively. How much (in INR) did Nitin give to Pravin?

• A. 697
• B. 870
• C. 770
• D. 847

Answer 1

Answer:

D. 847

Let the amount given to Pravin = ₹P
Then the amount given to Rishi = ₹(1617 − P)

Both invest at 10% p.a., compounded annually.

According to the question, the final amounts are equal:

$P(1.1)^{17} = (1617 - P)(1.1)^{18}$

Divide both sides by $( (1.1)^{17} ):$

$P = (1617 - P)\times 1.1$
$P = 1778.7 - 1.1P$
$2.1P = 1778.7$
$P = \frac{1778.7}{2.1} = 847$