SSC CGL 2024 Tier-I · 17 September 2024, Shift 3 · Quantitative Aptitude · Question 18 of 98

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.

A function of two variable varies directly with x and inversely with y. Determine function when x = 5 and y = 3. Given that, for x = 0 and y = 1, f = 15 and for x = 1 and y = 15, f = 2.

(a)2
(b)15
(c)5
(d)10

Answer

Why

Correct — D. The data fit the partly-direct, partly-inverse form f = ax + b⁄y, so pin down a and b first.

x = 0, y = 1 gives f = 15:
a(0) + b⁄1 = 15 → b = 15

x = 1, y = 15 gives f = 2:
a(1) + 15⁄15 = 2 → a + 1 = 2 → a = 1

So f = x + 15⁄y.
f(5, 3) = 5 + 15⁄3 = 5 + 5 = 10 → option (d).

Why the others are wrong

(a)
2 — 2 is the value of f at the second data point, x = 1 and y = 15. That was handed to you to fix the constants, not to answer with — the question asks for f at x = 5, y = 3.
(b)
15 — 15 is b, the constant of the inverse part, read straight off the first data point. It equals f only at that data point, where x = 0 and y = 1.
(c)
5 — 5 is the direct part alone, x = 5, with the inverse part 15⁄y dropped. Leaving it out throws away the datum f = 15 at x = 0, which is the very thing that fixes b.

Concept

'Varies directly with x and inversely with y' is written two ways, and the data decide which one is meant.

The product form f = kx⁄y carries a single constant. The additive form f = ax + b⁄y carries a direct part and an inverse part, each with its own constant.

Here f = 15 when x = 0. The product form forces f = 0 whenever x = 0, so it cannot fit. The additive form has two constants, and you have been given exactly two data points to fix them — a pair of linear equations.

The stem omits the word partly: read strictly, 'varies directly with x and inversely with y' names the joint variation f = kx⁄y. The datum f = 15 at x = 0 rules that reading out, so the intended function is the partly-direct, partly-inverse one, and it lands on the keyed value.

The paper also prints 'a function of two variable', its own slip, and 'Determine function' without an article. Quote it as it stands.

Key facts

Joint variation f = kx⁄y forces f = 0 whenever x = 0, which contradicts the given f = 15 at x = 0.
The partly-direct, partly-inverse form is f = ax + b⁄y, with two constants to be fitted.
The point (x = 0, y = 1) gives b = 15 and the point (x = 1, y = 15) then gives a = 1.
f = x + 15⁄y evaluates to 5 + 5 = 10 at x = 5, y = 3.

Study next

Fitting a partly-direct, partly-inverse relation from two data pointsJoint variation f = kxz and inverse-square variation, and how each behaves at zeroSolving a pair of linear equations in two unknowns by substitution

Common traps

Reading the stem as f = kx⁄y and then finding that no single constant fits both data points
Fitting the constants correctly and stopping there, answering with a or b instead of f(5, 3)
Cancelling 15⁄15 as 15 rather than 1, which turns a = 1 into a = −13

SSC hands you the constants indirectly and makes you fit them before answering the question actually asked. The same fit-then-evaluate shape runs in algebra at Quant Q.3 of this paper, where x + 1⁄x = 65⁄8 has to be turned into x − 1⁄x.

Related PYQs

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