A lent Rs. 5000 to B for a duration of 2 years and Rs. 3000 to C for a period of 4 years, both at the same simple interest rate.…

Question

A lent Rs. 5000 to B for a duration of 2 years and Rs. 3000 to C for a period of 4 years, both at the same simple interest rate. In total, he received Rs. 2200 as interest from both borrowers. What is the rate of interest per annum? (Expressed as a decimal, e.g. 0.1 for 10%.)

1. A. 0.1 (Correct answer)
2. B. 0.12
3. C. 0.15
4. D. 0.17

Correct Answer

Option A — 0.1

Detailed Solution & Explanation

The correct answer is 0.1.

Key Points

• Simple interest is P × R × T / 100, and the rate is common to both loans, so the two interests can be added:
  • From B: 5000 × 2 × R = 10,000 R
  • From C: 3000 × 4 × R = 12,000 R
• Total: 22,000 R = 2,200 (taking R as a decimal rate).
• R = 2,200 / 22,000 = 0.1, that is 10% per annum.
• Check: 5000 at 10% for 2 years gives ₹1,000, and 3000 at 10% for 4 years gives ₹1,200 — together ₹2,200 ✓.
• The answer is asked as a decimal, so 0.1 rather than 10 — the options are written to catch exactly that slip.

Additional Information

• Simple interest: SI = PRT/100 and Amount = P + SI; the interest is the same every year because it is always computed on the original principal.
• Compound interest: A = P(1 + R/100)^T. For two years the two differ by PR²/10⁴, a result asked in its own right.
• Where several loans share a rate, the rate can be factored out and the interests added — which is what turns this into a single linear equation.

प्रश्न (हिन्दी में)

A ने B को 2 वर्ष की अवधि के लिए 5000 रुपये और C को 4 वर्ष की अवधि के लिए 3000 रुपये समान साधारण ब्याज दर पर उधार दिए। कुल मिलाकर, उसे दोनों उधारकर्ताओं से ब्याज के रूप में 2200 रुपये मिले। प्रति वर्ष ब्याज की दर क्या है? (दशमलव में, जैसे 10% के लिए 0.1।)

1. A. 0.1
2. B. 0.12
3. C. 0.15
4. D. 0.17