A certain sum of money becomes ₹1000 in 2 years and ₹1100 in 4 years at simple…
2023
A certain sum of money becomes ₹1000 in 2 years and ₹1100 in 4 years at simple rate of interest. The rate of interest per annum is
Answer: B. \(5\frac{5}{9}\%\) — ConceptUnder simple interest, the interest earned each year is constant. If amounts after two different times are known, their difference equals the interest…
- A.
\(4\frac{3}{7}\%\)
- B.
\(5\frac{5}{9}\%\)
- C.
\(7\frac{4}{7}\%\)
- D.
\(6\frac{4}{9}\%\)
Show answer & explanation
Correct answer: B
Concept
Under simple interest, the interest earned each year is constant. If amounts after two different times are known, their difference equals the interest for the intervening years; also, annual interest = principal × rate / 100.
Application
The amount rises from ₹1000 after 2 years to ₹1100 after 4 years. Thus, interest for 2 years = ₹1100 − ₹1000 = ₹100, so annual interest = ₹100 ÷ 2 = ₹50.
Interest earned in the first 2 years = 2 × ₹50 = ₹100. Therefore, principal = ₹1000 − ₹100 = ₹900.
Rate per annum = (annual interest ÷ principal) × 100 = (₹50 ÷ ₹900) × 100 = 50/9% = \(5\frac{5}{9}\%\).
Cross-check
At 50/9% per annum, ₹900 earns ₹50 each year. After 2 years the amount is ₹900 + ₹100 = ₹1000, and after 4 years it is ₹900 + ₹200 = ₹1100, matching both given amounts.
Therefore, the rate of interest is \(5\frac{5}{9}\%\) per annum.