Simple Interest and Compound Interest Question 3 - CAT 2020

Let the total time elapsed since Veeru's investment be t years.

• Veeru's Total Balance after t years:

Veeru invests Rs. 10000 at a 5% simple annual interest rate.

Balanceᵥ = Principal + SI

Balanceᵥ = 10000 + (10000 × 5 / 100 × t) = 10000 + 500t

• Joy's Total Balance after t years:

Joy invests exactly 2 years after Veeru, so his money accumulates interest for (t − 2) years. He invests Rs. 8000 at a 10% simple interest rate.

Balanceⱼ = 8000 + (8000 × 10 / 100 × (t − 2))

Balanceⱼ = 8000 + 800(t − 2) = 8000 + 800t − 1600 = 6400 + 800t

• Equate the two balances:

10000 + 500t = 6400 + 800t

10000 − 6400 = 800t − 500t

3600 = 300t ⇒ t = 3600 / 300 = 12 years

Their balances will be equal 12 years after Veeru's initial investment.

Correct Answer: 12

💡 FundaMakers Tip:

Always define your time variable t based on the specific baseline requested in the final question prompt. Because this question specifically asks for the number of years after Veeru's investment, setting Veeru's timeline to t ensures your calculated result is the final answer, eliminating any off-by-two tracking errors.