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Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Updated On: Jan 15, 2026
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Solution and Explanation

We utilize the Simple Interest formula:

\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]

Step 1: Calculate Annual Interest for Both Individuals

Veeru's annual interest: \[ = \frac{10000 \times 5 \times 1}{100} = ₹500 \]

Joy's annual interest: \[ = \frac{8000 \times 10 \times 1}{100} = ₹800 \]

Step 2: Determine the Discrepancy

  • Annual interest difference = ₹800 - ₹500 = ₹300
  • Veeru's initial investment period was 2 years → Interest earned = ₹500 × 2 = ₹1000
  • Principal difference = ₹10000 - ₹8000 = ₹2000
  • Total difference (to equalize with Joy) = ₹1000 (interest gap) + ₹2000 (principal gap) = ₹3000

Step 3: Calculate Time to Bridge the ₹3000 Gap

\[ \text{Time} = \frac{₹3000}{₹300 \text{ per year}} = 10 \text{ years} \]

Final Answer:

Veeru has already invested for 2 years. To match Joy’s total investment, he needs to invest for an additional:

\[ 2 + 10 = \boxed{12 \text{ years}} \]

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