SSC CGL 2025 Tier-I · 12 September 2025, Shift 2 · General Intelligence and Reasoning · Question 23 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 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Two numbers are in ratio 7:9, and their sum is 128. Find the numbers.

(a)49, 79
(b)56, 72
(c)62, 66
(d)70, 58

Answer

Why

Correct — B. Split the sum into equal parts.

Rule: a ratio 7 : 9 means 7 parts and 9 parts of the same size.

Total parts: 7 + 9 = 16
One part: 128 ÷ 16 = 8
First number: 7 × 8 = 56
Second number: 9 × 8 = 72

Check: 56 + 72 = 128, and 56 : 72 = 7 : 9. That is 56, 72, option (b).

Why the others are wrong

(a)
49, 79 — Adds to 128, but 79 is prime, so it cannot be 9 × a whole number. 49 = 7 × 7 would need a partner of 9 × 7 = 63.
(c)
62, 66 — Adds to 128, but 62 : 66 = 31 : 33, not 7 : 9. The numbers are too close together for a 7-to-9 split.
(d)
70, 58 — Adds to 128, but the larger number comes first. 7 : 9 needs the first number smaller, and 70 : 58 reduces to 35 : 29.

Concept

A ratio fixes the shape of a split, not its size. 7 : 9 says the numbers are 7k and 9k for some k.

The sum pins down k: 7k + 9k = 16k = 128, so k = 8. Any ratio-and-sum problem yields to the same three moves: add the ratio terms, divide the total, multiply back.

All four options add to 128, so checking the sum eliminates nothing. The ratio is the test: reduce each pair by a common factor and see whether 7 : 9 appears.

Key facts

Numbers in the ratio a : b with sum S are S × a ÷ (a + b) and S × b ÷ (a + b).
128 ÷ 16 = 8, so the numbers are 56 and 72.
All four options sum to 128, so the ratio alone decides.

Study next

Ratio with a given difference instead of a sumThree-way ratios, such as 2 : 3 : 5 with a given totalReducing a pair to lowest terms to test a ratio

Common traps

Checking only the sum, when every option adds to 128.
Choosing 49, 79 because 49 = 7 × 7, when the partner must be 9 × 7 = 63.

The same set-up appears at 12 Sep 2025, 16:00, Reasoning Q.18: ratio 3 : 5, sum 64, answer 24 and 40. There too every option adds to 64, so the ratio is what separates them.

Related PYQs

No directly related past PYQ was found.