SSC CGL 2024 Tier-I · 24 September 2024, Shift 3 · Quantitative Aptitude · Question 13 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 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.

The ratio of two numbers is 2 : 5 and their difference is 210. The smaller number is ____________.

(a)60
(b)150
(c)350
(d)140

Answer

Why

Correct — D. Give the ratio a common multiplier and the difference names it.

Let the numbers be 2x and 5x.
Difference: 5x − 2x = 3x
So 3x = 210, giving x = 70

Smaller number = 2x = 2 × 70 = 140 → option (d).
Check: the larger is 5 × 70 = 350, and 350 − 140 = 210.

Why the others are wrong

(a)
60 — 60 is 2⁄7 of 210, the answer you get by treating 210 as the total to be shared in 2 : 5. It is a difference, so the parts to divide by number 3, not 7.
(b)
150 — 150 is the larger member of the pair 60 and 150, which differ by 90. Read instead as the smaller, its 2 : 5 partner would be 375 and the difference 225.
(c)
350 — 350 is the larger number, 5x at x = 70. The working is right and the slot is wrong — the stem asks for the smaller of the two.

Concept

A ratio fixes the shape of a pair, never its size. Write 2 : 5 as 2x and 5x, and one further fact — a sum, a difference, a product, one of the numbers — pins x down.

Here that fact is the difference, and 5x − 2x = 3x, so the ratio terms subtract exactly as the numbers do.

The shortcut worth carrying: the difference is spread over 5 − 2 = 3 parts, so one part is 210 ⁄ 3 = 70. The smaller number is two parts and the larger is five.

The stem ends in a blank rather than a question mark, so read carefully which of the two numbers is being asked for.

Key facts

A ratio a : b becomes ax and bx, and one extra condition fixes x.
Difference of the numbers = (b − a) parts, so one part = difference ⁄ (b − a).
For 2 : 5 with a difference of 210, one part is 70 and the numbers are 140 and 350.

Study next

Three-term ratios such as a : b : c with a given sumHow a ratio moves when a fixed quantity is added to both termsRatio of ages set a number of years before or after the present

Common traps

Dividing 210 by 5 or by 2 instead of by the difference of the parts, 3.
Treating 210 as the sum of the numbers and taking 2⁄7 of it, which gives 60.
Solving correctly and then reporting the larger number, 350.

Ratio with one extra condition is set as pure number work here and geometrically elsewhere. The same subtraction settles the angles of a triangle in the ratio 1 : 2 : 3 at Quant Q.3 of this paper, where the largest less the smallest comes to 60°.

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