SSC CGL 2024 Tier-I · 23 September 2024, Shift 1 · Quantitative Aptitude · Question 8 of 97

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.

The difference between the simple interests on the principal of ₹500 at an interest rate of 5% per annum for 3 years and 4% per annum for 4 years is:

(a)₹15
(b)₹5
(c)₹7.5
(d)₹10

Answer

Why

Correct — B. Simple interest is P × R × T ⁄ 100, and the principal is the same ₹500 in both cases.

First: 500 × 5 × 3 ⁄ 100 = ₹75
Second: 500 × 4 × 4 ⁄ 100 = ₹80

Difference = 80 − 75 = ₹5 → option (b)

The shortcut: on ₹500 every unit of R × T is worth ₹5, and 5 × 3 = 15 against 4 × 4 = 16 differ by just one unit.

Why the others are wrong

(a)
₹15 — ₹15 is the gap when both sums run for 3 years — ₹75 against ₹60. The second rate runs for 4 years, which lifts it to ₹80.
(c)
₹7.5 — ₹7.5 cannot arise here. Both R × T products are whole numbers, 15 and 16, so on a principal of ₹500 the difference has to be a whole multiple of ₹5.
(d)
₹10 — ₹10 would need the two R × T products to differ by 2. They differ by 1, because 5 × 3 = 15 and 4 × 4 = 16.

Concept

Simple interest is linear in both the rate and the time, so for a fixed principal only the product R × T matters.

Write it as P⁄100 × (R × T). On ₹500 that front factor is 5, so each unit of R × T is worth ₹5 of interest.

That is why a higher rate does not automatically mean more interest: 5% for 3 years gives 15 rate-years, 4% for 4 years gives 16, and the slower rate wins on the longer run.

The two schemes are compared on the same ₹500, so nothing has to be scaled — the whole item reduces to comparing 5 × 3 with 4 × 4.

Key facts

SI = P × R × T ⁄ 100.
₹500 at 5% for 3 years earns ₹75, and ₹500 at 4% for 4 years earns ₹80.
For a fixed principal, interest depends only on the product of rate and time, not on either alone.
Simple interest never compounds, so three years at 5% is exactly three times one year at 5%.

Study next

Comparing two simple-interest schemes through the product of rate and timeThe difference between simple and compound interest over the same periodFinding the rate or the time when the interest is given as a fraction of the sum

Common traps

Assuming the higher rate must earn the higher interest
Using one time period for both schemes
Reaching for the compound-interest formula on a question that says simple interest

SSC asks for the positive difference between two simple-interest runs, sometimes on the same principal and sometimes on two different ones — also asked 09 Sep 2024, 12:30, Quant Q.7 (₹5,000 at 15% for 3 years against ₹8,000 at 12% for 4 years).

Related PYQs

No directly related past PYQ was found.