Question

Mahesh has INR 1617 with him. He divided it amongst his sons Vijay and Ajay and asked them to invest it at 10% rate of interest compounded annually. It was seen that Vijay and Ajay got same amount after 13 and 14 years respectively. How much (in INR) did Mahesh give to Vijay?

• A. 870
• B. 697
• C. 770
• D. 847

Answer 1

Answer:

D. 847

Let the amounts invested be

Let:

Vijay’s principal = $(P_1)$

Ajay’s principal = $(P_2)$

We know:

$P_1 + P_2 = 1617$

Compound interest formula

The amount after (n) years at rate (r) (compounded annually) is:

$A = P (1 + r)^n$

Here, (r = 10% = 0.1)

We are told that after 13 and 14 years, the amounts are equal:
$P_1 (1.1)^{13} = P_2 (1.1)^{14}$
$P_1 (1.1)^{13} = P_2 (1.1)^{14} \implies P_1 = P_2 (1.1)$
$\implies P_2 = \frac{P_1}{1.1}$

Use the total sum

$P_1 + P_2 = 1617$

Substitute $(P_2 = \frac{P_1}{1.1})$:

$P_1 + \frac{P_1}{1.1} = 1617$
$P_1 \left(1 + \frac{1}{1.1}\right) = 1617$
$P_1 \left(1 + 0.9091\right) = 1617$
$P_1 (1.9091) = 1617$
$P_1 = \frac{1617}{1.9091}$ = 847

$P_2 = 1617 - 847 = 770$
Answer:

Mahesh gave INR 847 to Vijay.