Question:
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?
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 use the formula for Simple Interest:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Step 1: Calculate yearly interest for both
Veeru's yearly interest: \[ = \frac{10000 \times 5 \times 1}{100} = ₹500 \]
Joy's yearly interest: \[ = \frac{8000 \times 10 \times 1}{100} = ₹800 \]
Step 2: Determine the difference
- Difference in yearly interest = ₹800 - ₹500 = ₹300
- Veeru invested for 2 years initially → Interest earned = ₹500 × 2 = ₹1000
- Difference in principal = ₹10000 - ₹8000 = ₹2000
- Total difference (to match Joy) = ₹1000 (interest gap) + ₹2000 (principal gap) = ₹3000
Step 3: Time to cover 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, he must invest for:
\[ 2 + 10 = \boxed{12 \text{ years}} \]
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