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?

Correct — A. Let the rate be R% per annum and apply SI = P × R × T ÷ 100 to each loan.

Interest from B = 5000 × R × 2 ÷ 100 = 100R
Interest from C = 3000 × R × 4 ÷ 100 = 120R

Add them: 100R + 120R = 220R = 2200
Divide: R = 2200 ÷ 220 = 10% → option (a)

Why the others are wrong

• (b)
  12% — At 12% B pays 5000 × 12 × 2 ÷ 100 = ₹1200 and C pays 3000 × 12 × 4 ÷ 100 = ₹1440, a total of ₹2640, not ₹2200.
• (c)
  15% — At 15% the interest is 220 × 15 = ₹3300 (₹1500 from B and ₹1800 from C), well above the ₹2200 received.
• (d)
  17% — At 17% the interest is 220 × 17 = ₹3740 (₹1700 from B and ₹2040 from C), far more than the ₹2200 received.

Simple interest is P × R × T ÷ 100, earned only on the original sum, the same amount every year.

When two loans share one rate, add their principal × time products first: 5000 × 2 + 3000 × 4 = 22,000.

Each 1% of rate then earns 1% of 22,000, which is ₹220. Setting 220R = 2200 gives R = 10.

Key facts

• Simple interest = principal × rate × time ÷ 100.
• At one common rate, total interest = rate × (sum of principal × time for each loan) ÷ 100.
• Here 5000 × 2 + 3000 × 4 = 22,000, so each 1% of rate adds ₹220 of interest.

Common traps

• Using the total ₹8000 for an average of 3 years: 240R = 2200 gives R ≈ 9.2%. The loans run for different times, so each needs its own principal × time.

No directly related past PYQ was found.