SSC CGL 2025 Tier-I · 16 September 2025, Shift 2 · 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.

Seventy-five percent of a number is 15 more than two-thirds of that number. Find the number.

(a)120
(b)150
(c)180
(d)210

Answer

Why

Correct — C. Let the number be N and turn the words into an equation.

Seventy-five percent of N = 3⁄4 N
Equation: 3⁄4 N − 2⁄3 N = 15
Common denominator 12: 9⁄12 N − 8⁄12 N = 1⁄12 N

So 1⁄12 N = 15
Multiply by 12: N = 15 × 12 = 180 → option (c)

Why the others are wrong

(a)
120 — For 120 the gap is only 10: 75% of 120 = 90 and two-thirds of 120 = 80. The gap is always N⁄12, and 120⁄12 = 10.
(b)
150 — For 150 the gap is 12.5: 112.5 against 100. A gap of 15 needs N⁄12 = 15, which is 180, not 150.
(d)
210 — For 210 the gap is 17.5: 157.5 against 140. That overshoots 15, because the gap N⁄12 grows with N.

Concept

Convert both parts to fractions of the same number. 75% = 3⁄4, and 3⁄4 − 2⁄3 = 9⁄12 − 8⁄12 = 1⁄12.

So three-quarters of any number exceeds two-thirds of it by one-twelfth of the number. The stem says that gap is 15, so the number is 12 × 15.

Check by substitution: 75% of 180 = 135 and two-thirds of 180 = 120, and 135 − 120 = 15.

Key facts

75% = 3⁄4, and 3⁄4 − 2⁄3 = 1⁄12.
If a fraction f of a number equals k, the number is k ÷ f: here 15 ÷ 1⁄12 = 180.
Two-thirds is 66.67% to two decimals, not 66%.

Study next

Percentage–fraction equivalents such as 12.5% = 1⁄8, 33⅓% = 1⁄3 and 75% = 3⁄4Word problems of the form 'x% of a number is k more than y% of it'Finding a number from the difference between two of its fractions

Common traps

Writing 2⁄3 N − 3⁄4 N = 15 with the sides reversed, which gives a negative number. Three-quarters is the larger part.
Treating 75% − two-thirds as 75% − 66% = 9%. The exact gap is 1⁄12, about 8.33%.

14 Sep 2025, 12:30, Quant Q.4 is the same build in percentages: 45% − 30% = 15% of the number is 0.9, so the number is 0.9 ÷ 0.15 = 6.

Related PYQs

No directly related past PYQ was found.

Topic: Percentage — all 82 SSC CGL questions on it, every solved shift.