Question

Manoj has ₹1224 with him. He divided it amongst his sons Anand and Anil and asked them to invest it at 4% rate of interest compounded annually. It was seen that Anand and Anil got same amount after 17 and 18 years respectively. How much (in ₹) did Manoj give to Anil?

• A. 724
• B. 450
• C. 600
• D. 624

Answer 1

Answer:

C. 600

Let the amounts given to Anand and Anil be (A) and (B) respectively.

Rate of interest = 4% compounded annually

Given that the final amounts are equal:

$A(1.04)^{17} = B(1.04)^{18}$

Step 1: Simplify the equation

$B(1.04)^{18} = B(1.04)^{17} \times 1.04$

So,

$A(1.04)^{17} = B(1.04)^{17} \times 1.04$

Cancel $((1.04)^{17})$ on both sides:

A = 1.04B

Step 2: Use total money

$A + B = 1224$

Substitute (A = 1.04B):

$1.04B + B = 1224$
2.04B = 1224
$B = \frac{1224}{2.04}$
B = 600
Final Answer: Manoj gave ₹600 to Anil.