SSC CGL 2025 Tier-I · 19 September 2025, Shift 2 · Quantitative Aptitude · Question 3 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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If 12.5% of p is equal to 50% of q, what is the ratio p : q?

(a)1 : 4
(b)4 : 1
(c)1 : 2
(d)2 : 1

Answer

Why

Correct — B.
Write the percentages as fractions: 12.5% = 1⁄8 and 50% = 1⁄2

Set them equal: p⁄8 = q⁄2
Multiply both sides by 8: p = 4q
Divide both sides by q: p⁄q = 4⁄1

So p : q = 4 : 1 → option (b)

Why the others are wrong

(a)
1 : 4 — This is q : p, the ratio turned upside down. Test it: p = 1 and q = 4 give 12.5% of 1 = 0.125 against 50% of 4 = 2.
(c)
1 : 2 — p = 1, q = 2 gives 12.5% of 1 = 0.125 against 50% of 2 = 1. The two sides differ by a factor of 8.
(d)
2 : 1 — p = 2, q = 1 gives 0.25 against 0.5, so the sides still differ by a factor of 2. It is half the true ratio 4 : 1.

Concept

x% of A = y% of B means xA = yB, so A : B = y : x. The percentages swap sides.

Here x = 12.5 and y = 50, so p : q = 50 : 12.5 = 4 : 1.

It makes sense: p needs only a small slice (12.5%) to equal half of q, so p must be the bigger number.

Key facts

x% of A = y% of B gives A : B = y : x
12.5% = 1⁄8, so 12.5% of p is p⁄8
The quantity taken at the smaller percentage is the larger quantity

Study next

Three-term chains such as 25% of A = 20% of B = 10% of CFraction equivalents of percentages: 12.5% = 1⁄8, 37.5% = 3⁄8, 62.5% = 5⁄8

Common traps

Copying the percentages in the order they appear, 12.5 : 50, and answering 1 : 4

18 Sep 2025, 12:30, Quant Q.1 is the same form: 30% of m = 18% of n gives m : n = 18 : 30 = 3 : 5.

19 Sep 2025, 09:00, Quant Q.2 stretches it to three terms, 25% of A = 20% of B = 10% of C, keyed 4 : 5 : 10.

Related PYQs

No directly related past PYQ was found.

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