SSC CGL 2025 Tier-I · 15 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 11 September 2026.

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If a:b=5:3, then find (6a+2b):(6a−2b).

(a)3 : 2
(b)2 : 3
(c)5 : 3
(d)3 : 5

Answer

Why

Correct — A. Write both terms as multiples of one number k.

From a : b = 5 : 3, let a = 5k and b = 3k

Numerator: 6a + 2b = 30k + 6k = 36k
Denominator: 6a − 2b = 30k − 6k = 24k

Ratio: 36k : 24k = 36 : 24
Divide by 12: 3 : 2 → option (a)

Why the others are wrong

(b)
2 : 3 — 2 : 3 is the ratio upside down. The first term, 6a + 2b = 36k, is larger than the second, 6a − 2b = 24k, so the ratio must exceed 1.
(c)
5 : 3 — 5 : 3 is a : b, the ratio given, not the one asked. Substituting a = 5k and b = 3k turns the two expressions into 36k and 24k, which reduce to 3 : 2.
(d)
3 : 5 — 3 : 5 is b : a, the given ratio reversed. It uses neither expression, while (6a + 2b) : (6a − 2b) works out to 36 : 24.

Concept

A ratio a : b = 5 : 3 fixes the proportion, not the values, so write a = 5k and b = 3k. Every term of 6a + 2b and 6a − 2b then carries k, and k cancels in the ratio.

A shortcut divides both expressions by b. With a⁄b = 5⁄3, the ratio is (6 × 5⁄3 + 2) : (6 × 5⁄3 − 2) = 12 : 8 = 3 : 2.

Any value of k gives the same answer. With a = 5 and b = 3, 6a + 2b = 36 and 6a − 2b = 24, and 36 : 24 = 3 : 2.

Key facts

If a : b = m : n, put a = mk and b = nk for a non-zero k.
(pa + qb) : (pa − qb) depends only on a⁄b, so a and b themselves are never needed.
36 : 24 reduces by their HCF, 12, to 3 : 2.

Study next

Componendo and dividendo: if a⁄b = m⁄n, then (a + b)⁄(a − b) = (m + n)⁄(m − n)Joining linked ratios such as A : B and B : C into A : B : CRatios from equal percentages, such as 25% of A = 20% of B

Common traps

Writing the answer upside down: the sum 6a + 2b is the first term, so the larger number leads.
Picking 5 : 3 or 3 : 5 straight from the stem without substituting.

Setting each quantity equal to one k also solves 19 Sep 2025, 09:00, Quant Q.2: 25% of A = 20% of B = 10% of C = k gives A = 4k, B = 5k, C = 10k, so A : B : C = 4 : 5 : 10.

Related PYQs

No directly related past PYQ was found.

Topic: Ratio & Proportion — all 64 SSC CGL questions on it, every solved shift.