SSC CGL 2024 Tier-I · 25 September 2024, Shift 1 · Quantitative Aptitude · Question 2 of 100

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 10 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 salaries of P and Q together amount to ₹9,60,000. P and Q save 64% and 44%, respectively of their individual salaries. If P’s expenditure is 1.5 times Q’s expenditure, then what is the ratio of P’s salary to Q’s salary?

(a)2 : 3
(b)3 : 2
(c)3 : 7
(d)7 : 3

Answer

Why

Correct — D. Savings and expenditure are the two halves of one salary, so convert the savings rates into spending rates first.

P saves 64%, so P spends 36% → P's expenditure = 0.36P
Q saves 44%, so Q spends 56% → Q's expenditure = 0.56Q

The condition given is P's expenditure = 1.5 × Q's expenditure:
0.36P = 1.5 × 0.56Q = 0.84Q
P⁄Q = 0.84⁄0.36 = 84⁄36 = 7⁄3

So P : Q = 7 : 3, which is option (d). The ₹9,60,000 total is never needed.

Why the others are wrong

(a)
2 : 3 — Option (a), 2 : 3, makes Q the bigger earner. P spends 1.5 times what Q spends while parting with only 36% of salary against Q's 56%, so P's salary has to be the larger.
(b)
3 : 2 — Option (b), 3 : 2, is the multiplier 1.5 written as a ratio. It takes the expenditure relationship straight to the answer and skips the step that converts spending back into salary.
(c)
3 : 7 — Option (c), 3 : 7, is the right pair of numbers in the wrong order. The stem asks for P's salary to Q's salary, and P is the larger, so 3 : 7 answers Q : P.

Concept

Salary splits into exactly two parts, savings and expenditure, so a savings rate of 64% is a spending rate of 36%. Every question of this family turns on making that swap before writing an equation.

The condition then links the two spends, not the two salaries, and one equation in two unknowns is enough because only their ratio is asked.

The rupee total is supplied so the situation reads like a real payroll. It plays no part in a ratio.

If you do want the actual figures, the 7 : 3 split of ₹9,60,000 gives P ₹6,72,000 and Q ₹2,88,000, and 36% of 6,72,000 is indeed 1.5 times 56% of 2,88,000.

Key facts

Savings percentage and expenditure percentage of the same salary always add to 100%.
P spends 36% and Q spends 56%, so 0.36P = 1.5 × 0.56Q gives P : Q = 7 : 3.
Splitting ₹9,60,000 in the ratio 7 : 3 gives P ₹6,72,000 and Q ₹2,88,000.

Study next

Income and expenditure problems where both are given as ratiosPercentage change questions in which income and expenditure rise at different ratesRatio questions that supply a total the answer does not use

Common traps

Putting the savings rates 64% and 44% into the equation in place of the spending rates.
Setting up 1.5 the wrong way round, so that Q's spend is 1.5 times P's.
Hunting for a second equation because the ₹9,60,000 total looks as though it must be used.

SSC builds this family on the complement between saving and spending, and often prints a rupee total that plays no part in the answer. The same income-and-savings frame is set at 12 Sep 2024, 09:00, Quant Q.9 and at 26 Sep 2024, 16:00, Quant Q.12.

Related PYQs

No directly related past PYQ was found.