Question

Ashok has ₹1612 with him. He divided it amongst his sons Raj and Varun and asked them to invest it at 8% rate of interest compounded annually. It was seen that Raj and Varun got same amount after 15 and 16 years respectively. How much (in ₹) did Ashok give to Raj ?

• A. 687
• B. 837
• C. 875
• D. 775

Answer 1

Answer:

B. 837

Let the amounts given to Raj and Varun be (R) and (V) respectively.

Rate = 8% compounded annually

Given that their final amounts are equal:
$R(1.08)^{15} = V(1.08)^{16}$
Step 1: Simplify

$V(1.08)^{16} = V(1.08)^{15} \times 1.08$

So,

$R(1.08)^{15} = V(1.08)^{15} \times 1.08$

Cancel$((1.08)^{15})$ on both sides:

$R = 1.08V$

Step 2: Use total amount

$R + V = 1612$

Substitute (R = 1.08V):

$1.08V + V = 1612$
2.08V = 1612
$V = \frac{1612}{2.08}$
V = 775
Step 3: Find amount given to Raj

$R = 1.08 \times 775$
R = 837
Final Answer: Ashok gave ₹837 to Raj.