SSC CGL 2025 Tier-I · 20 September 2025, Shift 1 · Quantitative Aptitude · Question 16 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A bucket has 60 litres of a solution with sugar and water in the ratio 5:1. If 12 litres of the solution are replaced with water, what is the new ratio?

(a)2:1
(b)2:3
(c)3:1
(d)3:2

Answer

Why

Correct — A.
Split 60 L in 5 : 1: sugar 50 L, water 10 L
12 L of solution carries the same 5 : 1 split
Sugar removed: 10 L, water removed: 2 L

Left: sugar 40 L, water 8 L
Add 12 L water: 8 + 12 = 20 L of water
New ratio: 40 : 20 = 2 : 1 → option (a)

Why the others are wrong

(b)
2:3 — 2 : 3 puts water ahead of sugar. After the swap there are 20 L of water against 40 L of sugar, so sugar still leads.
(c)
3:1 — 3 : 1 with 40 L of sugar needs about 13.3 L of water. The bucket holds the 8 L left over plus the 12 L added, which is 20 L.
(d)
3:2 — 3 : 2 with 40 L of sugar needs about 26.7 L of water — more than the 20 L actually there after the 12 L top-up.

Concept

When you draw off part of a well-mixed solution, each ingredient leaves in the ratio it sits in the bucket. 12 L of a 5 : 1 solution carries out 10 L of sugar and 2 L of water.

Then only the added liquid changes: water goes up by 12 L, sugar does not. The total returns to 60 L (40 + 20), a quick check on the working.

Shortcut for one replacement with pure water: sugar keeps the fraction (60 − 12)⁄60 = 4⁄5 of its amount. Sugar = 50 × 4⁄5 = 40 L, and water is the rest of the 60 L.

Key facts

Removing part of a mixture takes out each ingredient in the mixture's own ratio
Replacing R litres of a V-litre mixture with water leaves the other ingredient at (V − R)⁄V of its amount
After n such replacements it is at ((V − R)⁄V)ⁿ of its amount

Study next

Repeated replacement: quantity left = original × (1 − R⁄V)ⁿRemoving a mixture and adding a different pure ingredientAlligation for mixing two solutions of different strengths

Common traps

Subtracting the whole 12 L from the sugar alone, as if only sugar left the bucket
Forgetting the water that left: keeping water at 10 L and adding 12 gives 22 L instead of 20 L

13 Sep 2025, 12:30, Quant Q.14 removes 15 L of a 3 : 2 milk-water mixture the same way (9 L milk, 6 L water) before adding 10 L of milk, keyed 23 : 12.

15 Sep 2025, 09:00, Quant Q.13 repeats a replacement twice: 100 × (9⁄10)² = 81 L of syrup left, keyed 81 : 19.

Related PYQs

No directly related past PYQ was found.

Topic: Ratio & Proportion — all 96 SSC CGL questions on it, every solved shift.