If the annual rate of simple interest increases from 10% to \(12\frac12\%\), a…
2023
If the annual rate of simple interest increases from 10% to \(12\frac12\%\), a man's annual income increases by ₹1,250. His principal (in ₹) is
Answer: B. 50,000 — ConceptUnder simple interest, the interest earned in one year is proportional to both the principal and the annual rate. When only the rate changes, the…
- A.
45,000
- B.
50,000
- C.
65,000
- D.
More than one of the above
- E.
None of the above
Show answer & explanation
Correct answer: B
Concept
Under simple interest, the interest earned in one year is proportional to both the principal and the annual rate.
When only the rate changes, the change in annual interest is ΔI = P × Δr / 100.
Application
Let P be the principal. The rate rises from 10% to 12.5%, so Δr = 12.5 − 10 = 2.5 percentage points.
The annual income rises by ₹1,250, hence 1,250 = P × 2.5 / 100.
Therefore P = 1,250 × 100 / 2.5 = ₹50,000.
Cross-check
At ₹50,000, the annual interest is ₹5,000 at 10% and ₹6,250 at 12.5%; the increase is ₹1,250.
Result
The principal is ₹50,000.