SSC CGL 2025 Tier-I · 23 September 2025, Shift 1 · Quantitative Aptitude · Question 7 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.

A square of side 10cm has a smaller square (of side 4cm) removed from one side. What is the ratio of the remaining area to the original?

(a)22:26
(b)21:25
(c)23:31
(d)24:25

Answer

Why

Correct — B. Work with areas, not sides.

Original area = 10 × 10 = 100 cm²
Removed area = 4 × 4 = 16 cm²
Remaining area = 100 − 16 = 84 cm²

Remaining : original = 84 : 100
Divide both by 4 = 21 : 25 → option (b)

Why the others are wrong

(a)
22:26 — 22 : 26 reduces to 11 : 13, about 0.846. The true ratio 84 : 100 is 0.84, and 22 : 26 does not simplify to it.
(c)
23:31 — 23 : 31 is about 0.742, which would mean roughly a quarter of the square was removed. 16 cm² out of 100 cm² is 16%.
(d)
24:25 — 24 : 25 is 96 : 100, which subtracts 4 cm², the small square's side, instead of its area of 16 cm².

Concept

A ratio of areas needs areas on both sides. A square's area grows with the square of its side, so a side of 4 against 10 is 2 : 5 in length but 4 : 25 in area.

Removing a piece changes the shape but not the arithmetic: the leftover area is the whole minus the piece, whatever the leftover looks like.

Reduce at the end by the highest common factor, here 4.

The stem does not say exactly where the small square is cut from. As long as it lies wholly inside the big square, the removed area is 16 cm² and the ratio stays 21 : 25.

Key facts

Area of a square = side².
A side ratio of 2 : 5 gives an area ratio of 4 : 25.
84 : 100 = 21 : 25 after dividing by 4.

Study next

Area of a path cut out of or around a rectangleRatio of areas of similar figures from the ratio of their sidesPercentage change in area when a side changes

Common traps

Subtracting the side instead of its area: 100 − 4 = 96 gives 24 : 25.
Writing the ratio the wrong way round, original : remaining = 25 : 21.

Taking a piece out and asking what is left also appears at 14 Sep 2025, 12:30, Quant Q.21, where a 616 m² circular pond sits in a 28 m square field: 784 − 616 = 168 m².

Related PYQs

No directly related past PYQ was found.

Topic: Ratio & Proportion — all 96 SSC CGL questions on it, every solved shift.