SSC CGL 2025 Tier-I · 14 September 2025, Shift 2 · General Intelligence and Reasoning · Question 25 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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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.

A two-digit number is 4 times the sum of its digits. If the digits are reversed, the new number is 18 more than the original. What is the number?

(a)24
(b)30
(c)36
(d)32

Answer

Why

Correct — A. Let the tens digit be x and the units digit y.

Rule: a two-digit number is 10x + y; reversed, it is 10y + x.

First condition: 10x + y = 4(x + y)
Expand: 10x + y = 4x + 4y
Collect terms: 6x = 3y, so y = 2x

Second condition: (10y + x) − (10x + y) = 18
Simplify: 9y − 9x = 18, so y − x = 2

Substitute y = 2x: 2x − x = 2, so x = 2 and y = 4
The number is 24: 4 × 6 = 24 and 42 − 24 = 18. Option (a).

Why the others are wrong

(b)
30 — 30 fails the first condition: its digit sum is 3, and 4 × 3 = 12, not 30. Reversed it is 03 = 3, smaller rather than 18 more.
(c)
36 — 36 passes the first condition, 4 × (3 + 6) = 36, but reversing gives 63, which is 27 more than 36, not 18.
(d)
32 — 32 fails the first condition: 4 × (3 + 2) = 20, not 32. Reversed it is 23, which is smaller.

Concept

Digit problems turn words into place value: a two-digit number with tens digit x and units digit y is 10x + y, and its reversal is 10y + x.

The gap between a number and its reversal is 9 × the difference of the digits: (10y + x) − (10x + y) = 9(y − x). So '18 more' means the units digit is 2 more than the tens digit.

A faster route: y = 2x allows 12, 24, 36 and 48, since the units digit cannot pass 9. Each is 4 times its digit sum, and 24 is the one whose digits differ by 2.

Key facts

A two-digit number with digits x (tens) and y (units) is 10x + y.
A number and its reversal differ by 9 times the difference of the digits.
24 = 4 × (2 + 4), and 42 − 24 = 18.

Study next

Digit problems that give the sum of a number and its reversal, which is 11 × (x + y)Two-digit numbers whose digits are in a given ratioThree-digit numbers written as 100x + 10y + z

Common traps

Choosing 36 because it passes the first condition, 4 × 9 = 36, without testing the reversal.
Subtracting the wrong way round, (10x + y) − (10y + x) = 18, which with y = 2x gives x = −2 and no answer.

A digit-sum condition also decides 14 Sep 2025, 09:00, Reasoning Q.19, where 39 fails because its digit sum, 12, does not divide it.

Related PYQs

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