Question

Mahesh has ₹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 15 and 16 years respectively. How much (in ₹) did Mahesh give to Vijay?

• A. 847
• B. 697
• C. 870
• D. 770

Answer 1

Answer:

A. 847

Step 1: Let the amounts given to Vijay and Ajay be:

• Vijay = (P₁)

• Ajay = (P₂)

Rate of interest (r = 10% = 0.1)
Time: Vijay = 15 years, Ajay = 16 years
Final amounts equal:

$P_1 (1.1)^{15} = P_2 (1.1)^{16}$

Step 2: Express (P₁) in terms of (P₂)

$P_1 (1.1)^{15} = P_2 (1.1)^{16} \implies P_1 = P_2 (1.1)$

Vijay got 1.1 times Ajay’s share

---

Step 3: Total amount distributed

$P_1 + P_2 = 1617$

$Substitute (P_1 = 1.1 P_2):$

$1.1 P_2 + P_2 = 1617 \implies 2.1 P_2 = 1617 percent$
$P_2 = \frac{1617}{2.1} = 770$

---

Step 4: Find Vijay’s share

$P_1 = 1.1 \cdot 770 = 847$

Vijay got ₹847
Ajay got ₹770