Two equal sums were borrowed at 8% simple interest per annum for periods of 2…
2023
Two equal sums were borrowed at 8% simple interest per annum for periods of 2 years and 3 years, respectively. The difference between the interest amounts was Rs.3080. What was the sum borrowed?
- A.
Rs.37950
- B.
Rs.38500
- C.
Rs.40700
- D.
Rs.67890
Show answer & explanation
Correct answer: B
Concept: For a fixed principal and rate, simple interest is directly proportional to time — SI = (P × R × T) / 100. So the difference between the interest earned over two different periods on the same sum depends only on the difference between those periods, not on the periods themselves: SI2 − SI1 = (P × R × (T2 − T1)) / 100.
Let the equal sum borrowed be Rs. P, at rate R = 8% per annum.
Interest for 3 years: SI3 = P × 8 × 3 / 100. Interest for 2 years: SI2 = P × 8 × 2 / 100.
Difference: SI3 − SI2 = P × 8 × (3 − 2) / 100 = 8P / 100 = 0.08P.
This difference is given as Rs.3080, so 0.08P = 3080, which gives P = 3080 / 0.08 = Rs.38500.
Cross-check: For P = Rs.38500 at 8%, the 2-year interest is 38500 × 8 × 2 / 100 = Rs.6160 and the 3-year interest is 38500 × 8 × 3 / 100 = Rs.9240. Their difference, 9240 − 6160 = Rs.3080, matches the given condition, confirming the sum borrowed was Rs.38500.