SSC CGL 2024 Tier-I · 9 September 2024, Shift 3 · Quantitative Aptitude · Question 18 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.

Ramesh has ₹18,000. He deposited ₹7,000 in a bank at the rate of 5% per annum and ₹6,000 in other bank at the rate of 6% per annum simple interest. If he received ₹1,160 as simple interest at the end of one year, then the rate of interest per annum on rest of the capital is equal to:

(a)10%
(b)9%
(c)8%
(d)11%

Answer

Why

Correct — B. The year's total interest is fixed at ₹1,160, so price the two named deposits first and hand the remainder to the third.

₹7,000 at 5% for one year → 7000 × 5⁄100 = ₹350
₹6,000 at 6% for one year → 6000 × 6⁄100 = ₹360
Interest from the two named deposits = 350 + 360 = ₹710

Interest still to be earned = 1160 − 710 = ₹450
Capital still unaccounted for = 18000 − 7000 − 6000 = ₹5,000

Rate = 450⁄5000 × 100 = 9% → option (b).

Why the others are wrong

(a)
10% — Test it back: ₹5,000 at 10% pays ₹500, so the year would yield 350 + 360 + 500 = ₹1,210 — fifty rupees more than the ₹1,160 the stem reports.
(c)
8% — 8% under-earns. ₹5,000 at 8% pays ₹400, giving a yearly total of ₹1,110, which falls ₹50 short of the ₹1,160 received.
(d)
11% — 11% overshoots badly: ₹5,000 at that rate pays ₹550 and the year's interest becomes ₹1,260, a full ₹100 above the figure given.

Concept

Simple interest is SI = P × R × T ⁄ 100, and at T = 1 the time factor disappears — the interest is just P × R⁄100.

Interest from separate deposits simply adds, so the ₹1,160 is the sum of three one-year interests, two of which the stem hands you outright.

That makes the question subtraction before division: strip out the known interest, strip out the known capital, and the unknown rate falls out of what is left.

The rate is recovered as R = (SI × 100) ⁄ (P × T).

The phrase 'rest of the capital' points at the ₹18,000, not the ₹1,160 — it is the ₹5,000 left after the two deposits, and the question assumes it too is earning simple interest for the same year.

Key facts

Simple interest for one year reduces to P × R⁄100, with no time factor to carry.
Interest from several deposits adds, so a stated total can be split across them.
The third deposit here is 18,000 − 7,000 − 6,000 = ₹5,000.
It must earn 1,160 − 350 − 360 = ₹450, which is 9% of ₹5,000.

Study next

Simple interest on a principal split across two or three different ratesAlligation on interest rates, and when it beats the long arithmeticRecovering the rate or the time from a stated interest amount

Common traps

Dividing the ₹450 by the whole ₹18,000 instead of by the ₹5,000 that earns it.
Subtracting only one of the two named deposits, leaving ₹11,000 as the balance.
Reading ₹1,160 as the interest from the third deposit alone.

SSC gives the combined interest and hides one rate, so the marks sit in the subtraction, not the interest formula. The same weighted-rate arithmetic runs in the opposite direction at Quant Q.3 of this shift, where four portfolio shares and their returns are combined into a single average return.

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