SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · General Intelligence and Reasoning · Question 18 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 11 September 2026.

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If the ratio of two numbers is 3:5 and their sum is 64, find the numbers

(a)24, 40
(b)20, 44
(c)18, 46
(d)16, 48

Answer

Why

Correct — A. Rule: one part = total ÷ (sum of the ratio terms).

Parts: 3 + 5 = 8
One part: 64 ÷ 8 = 8

First number: 3 × 8 = 24
Second number: 5 × 8 = 40

Check: 24 + 40 = 64, and 24 : 40 = 3 : 5 → option (a)

Why the others are wrong

(b)
20, 44 — 20 : 44 reduces to 5 : 11, not 3 : 5. The pair does sum to 64, but so does every option, so the sum alone decides nothing.
(c)
18, 46 — 18 : 46 reduces to 9 : 23, not 3 : 5. It meets the sum of 64 and fails the ratio.
(d)
16, 48 — 16 : 48 reduces to 1 : 3, not 3 : 5. The sum is right at 64, the ratio is not.

Concept

A ratio names parts, not the numbers themselves. 3 : 5 means the first number is 3 equal parts and the second is 5 of the same parts.

Add the terms to count all the parts (8), divide the total by that count to get one part (8), then multiply back.

Here all four options sum to 64, so the check that separates them is the ratio, not the sum.

With every option already summing to 64, dividing each pair by its highest common factor is the fastest check: 24 : 40 divided by 8 is 3 : 5.

Key facts

3 + 5 = 8 parts, and 64 ÷ 8 = 8 per part.
The numbers are 24 and 40.
All four options sum to 64, so the ratio is what separates them.

Study next

Dividing a sum among three people in a ratio such as 2 : 1 : 3Ratios given with the difference of the numbers instead of the sumAdding the same number to both terms of a ratio

Common traps

Checking only the sum, which every option passes.
Dividing 64 by 3 or by 5 instead of by 3 + 5.

The same one-part method decides 12 Sep 2024, 09:00, Quant Q.15, where ₹1,200 in the ratio 2 : 1 : 3 gives one part of ₹200 and shares of ₹400, ₹200 and ₹600.

Related PYQs

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