Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3…
2024
Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3 years, respectively. The difference in the interests was Rs. 3080. The sums borrowed were:
- A.
Rs. 37950
- B.
Rs. 38500
- C.
Rs. 40700
- D.
Rs. 67890
Show answer & explanation
Correct answer: B
Concept: When the same principal is lent at the same rate for two different time periods, the difference between the two simple-interest amounts equals the simple interest earned on that principal for just the difference in the two time periods. This follows directly from SI = (P × R × T) / 100, since SI grows linearly (uniformly) with time on a fixed principal and rate.
Application
Let the equal sum (principal) borrowed in each case be Rs. P, and the rate R = 8% per annum.
SI for 3 years = P × 8 × 3 / 100 = 24P/100, and SI for 2 years = P × 8 × 2 / 100 = 16P/100.
Difference of the two interests = 24P/100 − 16P/100 = 8P/100, i.e. exactly the simple interest on the sum for 1 year at 8% (since 3 − 2 = 1).
This difference is given as Rs. 3080, so 8P/100 = 3080, giving P = 3080 × 100 / 8 = 38500.
Cross-check: With P = Rs. 38500 at 8%, SI for 2 years = 38500 × 8 × 2 / 100 = Rs. 6160, and SI for 3 years = 38500 × 8 × 3 / 100 = Rs. 9240. Their difference = 9240 − 6160 = Rs. 3080, which matches the value given in the question.