SSC CGL 2024 Tier-I · 23 September 2024, Shift 2 · Quantitative Aptitude · Question 19 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.

A mango juice is made by mixing water and mango concentrate in the ratio 9 : 7. If x litres of water and 3x litres of mango concentrate is mixed in 160 litres of mango juice, then the new ratio becomes 13 : 14. What is the quantity of the new mango juice (in litres)?

(a)206
(b)216
(c)197
(d)212

Answer

Why

Correct — B. Turn the ratio into litres before touching x.

160 litres split 9 : 7 is 16 parts, so one part is 10 litres:
water = 90 L, concentrate = 70 L

Add x litres of water and 3x of concentrate, and impose the new ratio:

(90 + x) ⁄ (70 + 3x) = 13 ⁄ 14
14(90 + x) = 13(70 + 3x)
1260 + 14x = 910 + 39x

350 = 25x → x = 14
New volume = 160 + x + 3x = 160 + 56 = 216 litres → option (b)

Why the others are wrong

(a)
206 — 206 − 160 = 46, but the liquid poured in is x + 3x = 4x litres, so the new total must exceed 160 by a multiple of 4. It cannot land on 206.
(c)
197 — 197 is odd, while 160 + 4x is even for every whole x. 197 − 160 = 37 is not a multiple of 4, so no amount of pouring reaches this total.
(d)
212 — 212 needs x = 13. Put x = 13 back and the mix is 103 : 109, not 13 : 14. Only x = 14 gives 104 : 112, which reduces to 13 : 14.

Concept

A ratio is not a quantity. Convert first: 9 : 7 over 160 litres means 16 equal parts of 10 litres, so 90 litres of water and 70 of concentrate.

Only then does the addition make sense. Water becomes 90 + x, concentrate 70 + 3x, and the stated new ratio 13 : 14 gives you one linear equation in one unknown.

The question then asks for the volume, not for x, so the last step is 160 + 4x — the commonest place to lose the mark after doing the algebra correctly.

The new ratio keeps water first, matching the original 9 : 7 order. With x = 14 the mixture is 104 litres of water to 112 of concentrate, which is 13 : 14.

Key facts

In 160 litres split 9 : 7, one part is 10 litres, giving 90 litres of water and 70 of concentrate.
Adding x and 3x litres raises the total by 4x, so the new volume is 160 + 4x.
x = 14 makes the mixture 104 : 112, which reduces to 13 : 14.
The answer, 216 litres, is 160 + 4(14).

Study next

Converting a given ratio into actual quantities before any addition or removalBuilding one linear equation from a before-and-after ratioReplacement problems where liquid is drawn off and topped up with water

Common traps

Writing the new total as 160 + x instead of 160 + 4x.
Flipping the new ratio and giving water 14 parts instead of 13.
Answering with x = 14 rather than the quantity of juice the question asks for.

SSC states the starting mixture as a ratio and then disturbs it.

23 Sep 2024, 09:00, Quant Q.20 does it with 32 litres of milk and water at 5 : 3 and asks how much water reaches 50%. 10 Sep 2024, 16:00, Quant Q.11 compares two men's mixtures after each adds water.

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