SSC CGL 2024 Tier-I · 19 September 2024, Shift 3 · Quantitative Aptitude · Question 3 of 99

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 ratio of boys to girls initial in a college is 5 : 6. If 40 boys leave the college and 50 girls join the college, the ratio will become 8 : 11. Find the number of girls (initial) in the college.

(a)740
(b)640
(c)720
(d)860

Answer

Why

Correct — C. A 5 : 6 ratio only tells you the counts are 5x boys and 6x girls for some whole number x. Solve for x.

After the change the counts are 5x − 40 and 6x + 50, in the ratio 8 : 11:
(5x − 40)⁄(6x + 50) = 8⁄11
11(5x − 40) = 8(6x + 50)
55x − 440 = 48x + 400

7x = 840, so x = 120.

Girls at the start = 6x = 6 × 120 = 720 → option (c).

Check: 600 − 40 = 560 boys and 720 + 50 = 770 girls, and 560 : 770 = 8 : 11.

Why the others are wrong

(a)
740 — 740 fails the finishing check. It would leave 740 + 50 = 790 girls, but an 8 : 11 split needs the final number of girls to be a multiple of 11, and 790 is not.
(b)
640 — 640 fails at the start. A 5 : 6 ratio would make the boys 640 × 5⁄6 = 533⅓, and a college cannot hold a third of a boy.
(d)
860 — 860 breaks the same multiple-of-11 test: 860 + 50 = 910, and 11 × 82 = 902 leaves 8 over. Of the four options only 720 clears both checks.

Concept

A ratio is not a count. 5 : 6 fixes only the proportion, so the counts must be written as 5x and 6x and the multiplier x is what the equation solves for.

Absolute changes — 40 leaving, 50 joining — act on the counts, never on the ratio terms. That is why you cannot subtract 40 from the 5. Convert to 5x and 6x, apply the changes, then set the new ratio equal to 8 : 11 and cross-multiply.

The stem's "initial" (printed as "initial" rather than "initially") marks which of the two girl counts is wanted: the one before the 50 join, so 720 and not 770.

Key facts

A 5 : 6 ratio means the counts are 5x and 6x for a whole number x, and here x = 120.
Adding or removing a fixed number of people changes the counts, not the ratio terms.
If the final ratio is 8 : 11 in lowest terms, the final number of girls must be a multiple of 11, as 770 = 11 × 70 is.
The initial counts are 600 boys and 720 girls, totalling 1320.

Study next

Ratio problems where the change is itself a percentage rather than a fixed numberThree-term ratios a : b : c with one term alteredMixture and alligation, which uses the same 5x setup for milk and water

Common traps

Solving for x and reporting 120 instead of the number of girls
Subtracting 40 from the ratio term 5 rather than from 5x
Answering with the boys' count of 600, or with the final girls' count of 770

The same 5x setup carries over to mixtures: at 23 Sep 2024, 09:00, Quant Q.20 a 32 litre mixture holds milk and water in 5 : 3 and the question asks how much water to add to move the ratio.

Related PYQs

No directly related past PYQ was found.