SSC CGL 2024 Tier-I · 11 September 2024, Shift 2 · Quantitative Aptitude · Question 3 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.

S borrowed some amount from R and promised to pay him 8% interest. Then S invested the borrowed amount in a scheme, upon which he earned a profit of 5% after paying R, the principal amount with interest. How much percentage R would have gained, if he would have invested in the scheme directly?

(a)14%
(b)13%
(c)14.4%
(d)13.4%

Answer

Why

Correct — B. Take the borrowed sum as ₹100 — only percentages are given, so the base is yours to choose.

What S owes R, principal plus 8% interest:
100 + 8 = ₹108

S's own profit is 5% of the ₹100 he put into the scheme:
= ₹5

So the scheme returned 108 + 5 = ₹113 on an investment of ₹100.

R investing directly would keep all of that: a gain of 13% → option (b).

Why the others are wrong

(a)
14% — Fourteen is a decoy round number. The scheme's return is the 8% that leaves S's hands plus the 5% that stays in them, both measured on the same ₹100, and 8 + 5 is 13.
(c)
14.4% — 14.4 has no route through these numbers. It sits beside the 13.4 decoy so that a mis-based calculation still finds something to pick. The scheme pays ₹113 on ₹100.
(d)
13.4% — 13.4 comes from charging S's 5% profit on the ₹108 he repaid: 108 × 1.05 = 113.4. But the profit is on what S invested, the ₹100 he borrowed, so the scheme returns ₹113.

Concept

This is a middleman chain. S borrows at one rate, invests at a higher one, and keeps the difference. The scheme's true return is everything S receives, not merely what he retains.

Return to the scheme = interest handed to R + profit kept by S.

Percentages may be added only when they sit on the same base. Here both the 8% and the 5% are quoted on the amount borrowed, so 8 + 5 = 13 is legitimate. Change either base and the shortcut breaks.

The question does not spell out what the 5% profit is a percentage of. The key reads it as 5% of the borrowed amount, which puts both percentages on the same ₹100 and gives a clean 13%.

Say the base out loud before you add two percentages.

Key facts

Percentages may be added only when they are taken on the same base.
The scheme's return equals the interest S paid out plus the profit S kept.
With no absolute figures given, set the unknown amount to ₹100 and read the answer off directly.
8% interest plus a 5% profit on the same ₹100 is a 13% total return.

Study next

Successive percentage change, where the second percentage sits on a changed baseSimple interest, where the principal stays the base throughoutEffective gain when a middleman borrows at one rate and invests at another

Common traps

Compounding the 5% on ₹108 instead of taking it on ₹100
Reading the 5% as R's gain rather than S's
Treating 'after paying R' as meaning the profit is measured on what is left over

SSC likes the borrow-invest-keep-the-difference chain because it looks like interest and is really percentage bookkeeping. Percentage arithmetic runs through this shift: Quant Q.19 puts cost price at 75% of marked price with a 15% discount, and Quant Q.20 raises a salary by 25% and then cuts it by 12%.

Related PYQs

No directly related past PYQ was found.