SSC CGL 2024 Tier-I · 23 September 2024, Shift 2 · Quantitative Aptitude · Question 10 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 10 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 simple interest on a sum for 8 years is three-fifth of the sum. The rate of interest per annum is:

Answer

Why

Correct — B. Call the sum P. The interest is given as a fraction of the sum, so P cancels and its value is never needed.

SI = P × R × T ⁄ 100, with SI = 3⁄5 P and T = 8
3⁄5 P = P × R × 8 ⁄ 100

Cancel P: 3⁄5 = 8R ⁄ 100
R = 300 ⁄ (5 × 8) = 7.5

The rate is 7½% per annum → option (b).

Why the others are wrong

(a)
9% for 8 years earns 9 × 8 = 72% of the sum, i.e. 18⁄25 of it. The question fixes the interest at three-fifths, which is 60%.
(c)
6% for 8 years earns only 48% of the sum, well short of the 60% the stem states. That rate would need 10 years to reach three-fifths.
(d)
5½% over 8 years earns 44% of the sum. To reach 60% in the same 8 years the rate has to be higher, not lower.

Concept

Simple interest is linear in both rate and time: SI = P × R × T ⁄ 100. Divide both sides by P and the principal disappears, leaving SI⁄P = R × T ⁄ 100.

So whenever the interest is quoted as a fraction or percentage of the sum itself, the problem reduces to one equation in R and T. Here SI⁄P = 3⁄5 = 60%, so R × T = 60, and with T = 8 the rate is 60 ⁄ 8 = 7.5%.

That is why no principal appears in the question and none is needed in the answer.

The four options are printed as small images rather than text, and option (b) shows the mixed fraction 7½%, which is the same number as 7.5%.

Key facts

SI = P × R × T ⁄ 100, so the interest expressed as a fraction of the principal is R × T ⁄ 100.
Interest equal to 3⁄5 of the sum means the product R × T equals 60.
At 7.5% simple interest a sum earns 60% of itself in 8 years and doubles in 13⅓ years.

Study next

Finding the time in which a sum becomes n times itself under simple interestThe same sum lent in two parts at two different simple-interest ratesCompound interest on identical data, where the principal no longer cancels

Common traps

Reading three-fifth of the sum as the amount rather than as the interest.
Swapping R and T, and solving as though the rate were 8%.
Hunting for a decimal 7.5% among the options and missing the mixed fraction 7½%.

SSC reuses this one-line template with the fraction and the number of years changed. The same stem with six years instead of eight is asked 25 Sep 2024, 09:00, Quant Q.13, where 60 ⁄ 6 gives 10%.

Related PYQs

No directly related past PYQ was found.