SSC CGL 2024 Tier-I · 9 September 2024, Shift 2 · Quantitative Aptitude · Question 22 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 5 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.

If x varies inversely as y and x = 2 when y = 6, then the value of y when x = 3 is:

(a)3
(b)4
(c)2
(d)6

Answer

Why

Correct — B. 'Varies inversely' fixes the product, not the ratio: x ∝ 1/y means xy = k.

Find k from the pair you are given:
k = 2 × 6 = 12

Now put x = 3 into xy = 12:
y = 12 ÷ 3 = 4 → option (b)

Direction check: x rose from 2 to 3, so y must fall. Anything at or above 6 is wrong before you calculate.

Why the others are wrong

(a)
3 — 3 is the new value of x written into the answer slot. The question asks what y becomes once x reaches 3, which is 12 ÷ 3.
(c)
2 — 2 is x's starting value. Nothing in the problem sends y to a number x once held — the invariant is the product xy = 12, not either variable on its own.
(d)
6 — 6 is y left unchanged. With x up from 2 to 3, y has to fall; holding y at 6 would make the product 18 instead of the fixed 12.

Concept

Two quantities vary inversely when their product is constant: x = k/y, so x₁y₁ = x₂y₂.

Direct variation fixes the ratio instead: x₁/y₁ = x₂/y₂. One word in the question — 'inversely' — decides which setup you write, and the rest is a single constant.

The same structure runs through most arithmetic word problems: men and days, speed and time over a fixed distance, pipes and hours. More of one means proportionally less of the other, with the product standing for the fixed job.

Key facts

Inverse variation means the product is constant: xy = k, so x₁y₁ = x₂y₂.
Here 2 × 6 = 3 × y, which gives y = 4.
Direct variation on the same numbers would fix x/y = 1/3 and give y = 9 at x = 3.
Multipliers are reciprocal: x multiplied by 3/2 forces y to be multiplied by 2/3.

Study next

Joint and combined variation, e.g. z varies directly as x and inversely as y²Time and work, where rate and time vary inversely for a fixed jobSpeed, distance and time, where speed and time vary inversely over a fixed distance

Common traps

Setting up 2/6 = 3/y, the direct-variation proportion, which returns 9.
Answering with the value of x that was just substituted.
Reading 'inversely' as swapping the two numbers rather than as fixing their product.

Tier-I keeps this to one line. The harder versions replace y with y² or √y, so the constant becomes xy² or x√y — the product rule is unchanged, only the power moves.

Quant Q.25 of this shift (09 Sep 2024, 12:30) is the same constant-product idea applied to pipes filling a tank.

Related PYQs

No directly related past PYQ was found.