A sum of ₹ 4,080 is divided between Ajay and Vijay in such a way that when…
2025
A sum of ₹ 4,080 is divided between Ajay and Vijay in such a way that when invested on compound interest, the amount Ajay receives after 10 years is equal to the amount Vijay receives after 11 years, the interest being compounded annually at 4% per annum. The share of Ajay is:
- A.
2,000
- B.
2,080
- C.
2,280
- D.
2,200
- E.
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Correct answer: B
To find the share of Ajay, we need to divide the total amount of 4,080 between Ajay (let's call his share A) and Vijay (let's call his share V) such that their amounts after specific periods are equal.
Step-by-Step Analysis
Define the equation:
The amount Ajay receives after 10 years is A * (1 + 4/100)^10.
The amount Vijay receives after 11 years is V * (1 + 4/100)^11.
Given: A * (1.04)^10 = V * (1.04)^11
Simplify the ratio:
Divide both sides by (1.04)^10:
A = V * (1.04)^1
A = V * 1.04
A / V = 1.04 / 1 = 104 / 100 = 26 / 25
Divide the total sum:
The ratio of Ajay's share to Vijay's share is 26 : 25.
Total parts = 26 + 25 = 51.
Ajay's share (A) = (26 / 51) * 4,080.
Final Calculation:
4,080 / 51 = 80.
A = 26 * 80 = 2,080.
Ajay's share is 2,080, which corresponds to Option 2.