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

Mahesh gave INR 847 to Vijay.

Step-by-Step Solution

1. Formulate the Equation

Let Vijay's share be $V$ and Ajay's share be $A$.

• Total amount equation:
  $V + A = 1617$

• The formula for compound interest amount is:
  $A = P \left(1 + \frac{R}{100}\right)^T$

Given that their final amounts are equal:
$V \left(1 + \frac{10}{100}\right)^{13} = A \left(1 + \frac{10}{100}\right)^{14}$

2. Simplify the Ratio

Simplify the base term: $\left(1 + \frac{10}{100}\right) = 1.1 = \frac{11}{10}$

Substitute this back into the equation:
$V \times (1.1)^{13} = A \times (1.1)^{14}$

Divide both sides by $(1.1)^{13}$:
$V = A \times (1.1)^1$

$V = A \times \frac{11}{10}$

$\frac{V}{A} = \frac{11}{10}$

The ratio of Vijay's share to Ajay's share is 11 : 10.

3. Calculate Vijay's Share

• Total Ratio Parts: $11 + 10 = 21\text{ parts}$

• Value of 21 Parts: INR 1617

• Value of 1 Part: $\frac{1617}{21} = 77$

• Vijay's Share (11 Parts): $11 \times 77 = \mathbf{847}$