SSC CGL 2024 Tier-I · 12 September 2024, Shift 1 · Quantitative Aptitude · Question 9 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

The incomes of P, Q and R are in the ratio 10 : 12 : 9 and their expenditures are in the ratio 12 : 15 : 8. If Q saves 25% of his income, then what is the ratio of the savings of P, Q and R?

(a)21 : 14 : 15
(b)15 : 14 : 21
(c)21 : 15 : 14
(d)14 : 15 : 21

Answer

Why

Correct — D. Incomes and expenditures are on different scales, so they need different variables: incomes 10x, 12x, 9x and expenditures 12y, 15y, 8y.

Q saves 25% of income, so Q spends 75% of 12x = 9x
Q's expenditure is also 15y, so 15y = 9x → y = 0.6x

P spends 12y = 7.2x → saves 10x − 7.2x = 2.8x
Q saves 12x − 9x = 3x
R spends 8y = 4.8x → saves 9x − 4.8x = 4.2x

Ratio 2.8 : 3 : 4.2, multiplied by 5, is 14 : 15 : 21 — option (d).

Why the others are wrong

(a)
21 : 14 : 15 — This gives P the largest saving. P spends 12y = 7.2x against an income of 10x, saving 2.8x, which is the smallest of the three.
(b)
15 : 14 : 21 — This makes P save more than Q. P saves 2.8x and Q saves 3x, so P cannot lead Q however the other two are placed.
(c)
21 : 15 : 14 — This leaves R the smallest. R spends 8y = 4.8x on an income of 9x, saving 4.2x — the largest saving of the three.

Concept

Two ratios describing the same three people carry two independent scale factors. Writing incomes as 10x, 12x, 9x and expenditures as 12y, 15y, 8y keeps them separate until a given fact links them.

The link here is Q. Saving 25% of income means spending 75% of 12x, which is 9x, and that same expenditure is 15y — so y = 0.6x.

Once y is in terms of x, every expenditure is comparable with every income, and saving = income − expenditure gives the three savings directly.

Any one person's saving would have done as the link; the paper chose Q because 25% of 12 is a whole number.

Key facts

Saving = income − expenditure, so a savings ratio needs both ratios on one common scale.
Q spending 75% of 12x = 9x, set equal to 15y, fixes y = 0.6x.
The savings are P = 2.8x, Q = 3x and R = 4.2x.
Multiplying 2.8 : 3 : 4.2 by 5 clears the decimals to 14 : 15 : 21.

Study next

Income-expenditure items where a saving is given as an amount rather than a percentageTwo ratios joined through one shared member, and when they can be merged into a single chainPercentage increase applied to one term of a ratio while the others hold

Common traps

Using a single variable for both ratios, which silently assumes incomes and expenditures share a scale
Applying Q's 25% to Q's expenditure instead of Q's income
Answering in the wrong order, since the four options here are permutations of 14, 15 and 21

Two ratios plus one anchoring fact about a single person is the shape to recognise. Also asked 26 Sep 2024, 16:00, Quant Q.12, where incomes are 2 : 9 : 3, expenses 3 : 9 : 5, and A's saving is half of A's income.

Here the four options are permutations of the same three numbers, so order alone decides the mark. At that 26 Sep item they are four different ratios, and the arithmetic decides it.

Related PYQs

No directly related past PYQ was found.