SSC CGL 2025 Tier-I · 22 September 2025, Shift 1 · Quantitative Aptitude · Question 7 of 98

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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Two numbers are in the ratio 6:5. If the difference between them is 11, find the numbers.

(a)66 and 55
(b)60 and 49
(c)72 and 61
(d)88 and 77

Answer

Why

Correct — A. Write the two numbers as 6k and 5k for some multiplier k.

Difference: 6k − 5k = k
Set it equal to 11: k = 11
Numbers: 6 × 11 = 66 and 5 × 11 = 55 → option (a)

Check: 66 : 55 reduces to 6 : 5 on dividing by 11, and 66 − 55 = 11.

Why the others are wrong

(b)
60 and 49 — The difference is 11, but 60 : 49 is not 6 : 5. With 60 as the 6-part, the 5-part would have to be 50.
(c)
72 and 61 — The difference is 11, but 72 : 61 is not 6 : 5. With 72 as the 6-part, the 5-part would have to be 60.
(d)
88 and 77 — The difference is 11, but 88 : 77 reduces to 8 : 7 on dividing by 11, not 6 : 5.

Concept

A ratio a : b fixes the proportion, not the size, so write the quantities as ak and bk for an unknown multiplier k.

A stated total or difference then pins k. Here the difference is (6 − 5)k = k, so the difference itself is the multiplier.

In general, with difference D, k = D ⁄ (a − b).

All four options differ by exactly 11, so checking the difference eliminates nothing. The ratio check is what separates them.

Key facts

Numbers in the ratio a : b can be written as ak and bk.
If their difference is D, then k = D ⁄ (a − b).
If their sum is S, then k = S ⁄ (a + b).
To test a pair, divide both by their HCF: 66 and 55 share 11 and leave 6 and 5.

Study next

Ratio problems where the sum, not the difference, is givenThree-term ratios with a given total or averageRatios that change when the same number is added to both terms

Common traps

Checking the difference alone: every option here differs by 11.
Taking 11 as one of the numbers instead of as the multiplier k.

Here the difference is given and both numbers are asked. A two-term ratio with a given difference is also set at 24 Sep 2024, 16:00, Quant Q.13 (2 : 5, difference 210), and a three-term ratio with a given average at 20 Sep 2025, 12:30, Quant Q.17.

Related PYQs

No directly related past PYQ was found.

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