SSC CGL 2024 Tier-I · 17 September 2024, Shift 2 · Quantitative Aptitude · Question 21 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

What is the rate of interest per annum for simple interest at which ₹1,040 amounts to ₹1,230 in 1 1⁄2 years?

Answer

Why

Correct — C. The stem has ₹1,040 growing to ₹1,230 in 1½ years at simple interest. Interest is the amount minus the principal.

SI = 1,230 − 1,040 = ₹190

R = (SI × 100) ⁄ (P × T)
= (190 × 100) ⁄ (1,040 × 1.5)
= 19,000 ⁄ 1,560

19,000 ⁄ 1,560 = 475 ⁄ 39 = 12 7⁄39 % per annum → option (c), which prints 12 7⁄39 %.

Why the others are wrong

(a)
Option (a) is 11 7⁄39 % = 436⁄39 %. On ₹1,040 for 1½ years that earns ₹174.40, so the sum would reach ₹1,214.40 and not the ₹1,230 given.
(b)
Option (b) is 13 7⁄39 % = 514⁄39 %, which earns ₹205.60 over the same period. That amounts to ₹1,245.60 — ₹15.60 too much.
(d)
Option (d) is 10 7⁄39 % = 397⁄39 %, giving ₹158.80 of interest and an amount of ₹1,198.80, which falls ₹31.20 short of ₹1,230.

Concept

Simple interest is charged on the original principal for the whole term: SI = P × R × T ⁄ 100, and the amount is P + SI.

Rearranged for the rate that gives R = (SI × 100) ⁄ (P × T). The only real trap in setting it up is remembering that ₹1,230 is the amount, so the interest has to be extracted first.

Time must be in years to match a per-annum rate, so 1½ years enters the formula as 1.5 or 3⁄2 — never as 18 months.

All four printed options carry the same fraction, 7⁄39, so only the whole-number part decides the item.

Dividing to two decimals is therefore enough: 19,000 ⁄ 1,560 ≈ 12.18, and you can stop. The exact mixed number only matters when two options share a whole number.

Key facts

SI = P × R × T ⁄ 100, and Amount = P + SI.
Rearranged for the rate, R = (SI × 100) ⁄ (P × T).
Here SI = 1,230 − 1,040 = ₹190 and P × T = 1,040 × 1.5 = 1,560.
19,000 ⁄ 1,560 simplifies to 475 ⁄ 39, which is 12 7⁄39 %.

Study next

Rearranging the simple-interest formula for rate, time and principal in turnHandling part-year terms such as 1½ years, 8 months or 13 months against a per-annum rateTelling simple interest from compound interest when a stem supplies only P, A and T

Common traps

Using ₹1,230 as the interest instead of subtracting the principal first
Entering 1½ years as 18, the number of months, against a per-annum rate
Rounding 12.18 down to 12 and then hunting for a plain 12% option that is not printed

SSC supplies three of the four quantities — principal, amount and time — and asks for the fourth.

The mirror image, fixing the rate and asking for the time, runs at 17 Sep 2024, 16:00, Quant Q.25 (₹7,200 to ₹8,928 at 8%) and at 11 Sep 2024, 12:30, Quant Q.25 (₹8,400 to ₹11,928 at 7%). A rate-from-amount version over ten years is at 19 Sep 2024, 12:30, Quant Q.25.

Related PYQs

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