A principal amount of ₹1,000 yields a simple interest of ₹180 over a period of 2 years. What is the annual rate of simple interest?
- (a)8 %
- (b)9 %
- (c)7 %
- (d)6 %
Answer
Why
Correct — B.
Rule: SI = P × R × T ⁄ 100, so R = SI × 100 ⁄ (P × T).
SI × 100 = 180 × 100 = 18,000
P × T = 1,000 × 2 = 2,000
R = 18,000 ⁄ 2,000 = 9% a year → option (b).
Why the others are wrong
- (a)8 % — 8% gives 1,000 × 8 × 2 ⁄ 100 = ₹160 over two years, ₹20 short of the ₹180 stated.
- (c)7 % — 7% gives 1,000 × 7 × 2 ⁄ 100 = ₹140 over two years, ₹40 short of ₹180.
- (d)6 % — 6% gives 1,000 × 6 × 2 ⁄ 100 = ₹120 over two years, only two-thirds of ₹180.
Concept
Simple interest is charged on the original principal only, so it adds the same amount every year.
Here ₹180 over 2 years is ₹90 a year. ₹90 on ₹1,000 is 90⁄1,000 = 9⁄100, a rate of 9% a year, which is the same answer without the formula.
Key facts
- SI = P × R × T ⁄ 100, with R in % a year and T in years.
- Under simple interest the interest is the same every year, here ₹90.
- Amount = Principal + SI, so this sum grows to ₹1,180 in 2 years.
Study next
Common traps
- Forgetting to divide by the 2 years, which gives 18%
- Using the amount, ₹1,180, in place of the interest, ₹180
14 Sep 2025, 16:00, Reasoning Q.22 asks for the rate from a growth factor instead: a sum that becomes 2.5 times itself in 10 years earns 1.5 times itself as interest, keyed 15% a year.
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