UPSC Prelims 2010 Q114: Science & Technology – Quantitative Aptitude

UPSC Prelims 2010, General Studies Paper I · Science & Technology

The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2·50. What is the difference between their rates?

Answer: (a) 0·25%

Explanation

Finding the interest-rate difference between two banks

The simple interest difference on the same principal and time period reveals the rate difference directly.

Step	Calculation
SI formula	SI = (P × R × T) / 100
Difference in SI	For the same P and T, the difference depends only on the difference in rates (ΔR)
Given values	P = ₹500, T = 2 years, Difference in SI = ₹2.50
Equation	2.50 = (500 × ΔR × 2) / 100
Solve	2.50 = 10 × ΔR → ΔR = 0.25%

Why this works:

Point	Detail
Same P, T	Only ΔR (rate difference) explains the SI gap
Direct proportionality	SI difference scales linearly with rate difference

Answer: (a) 0.25%.

(a) CORRECT. Solving 2.50 = (500 × ΔR × 2)/100 gives ΔR = 0.25%.
(b) Incorrect. 0.5% does not satisfy the given SI-difference equation.
(c) Incorrect. 1% would produce a much larger SI difference than ₹2.50.
(d) Incorrect. 2.5% would produce an even larger SI difference, far exceeding ₹2.50.

With the same principal and time, the simple interest difference equals (P × ΔR × T)/100 — solving 2.50 = (500 × ΔR × 2)/100 gives ΔR = 0.25%.

₹500, 2 years, SI difference ₹2.50 → rate difference = 0.25%.

Forgetting that with identical principal and time, the SI formula isolates the rate difference directly.
Making an algebraic slip while solving for ΔR.
Confusing this with a compound interest problem, which would require a different approach.

When principal and time are identical across two SI calculations, the SI difference directly reveals the rate difference via (P×ΔR×T)/100.

R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Simple Interest)
NCERT Class VIII Mathematics — Comparing Quantities