SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · Quantitative Aptitude · Question 4 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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The expenditure of a household on food, clothing, and entertainment is in the ratio 2 : 4 : 4. In the coming year, the cost of food is expected to fall by 10%, clothing to rise by 5%, and entertainment to fall by 15%. What is the percent change (increase or decrease) in the total household expenditure?

(a)5% decrease
(b)6% increase
(c)6% decrease
(d)5% increase

Answer

Why

Correct — C. Read the ratio 2 : 4 : 4 as amounts out of a total of 10.

Food falls 10%: 2 × 0.90 = 1.8 (−0.2)
Clothing rises 5%: 4 × 1.05 = 4.2 (+0.2)
Entertainment falls 15%: 4 × 0.85 = 3.4 (−0.6)

New total: 1.8 + 4.2 + 3.4 = 9.4
Change: 9.4 − 10 = −0.6, and −0.6 ÷ 10 × 100 = −6%
A 6% decrease → option (c)

Why the others are wrong

(a)
5% decrease — Right direction, wrong size. A 5% fall would leave the total at 9.5, but the three new amounts add to 9.4, a fall of 0.6 on 10.
(b)
6% increase — Right size, wrong sign. Food's −0.2 and clothing's +0.2 cancel, and entertainment's −0.6 is left over, so spending falls.
(d)
5% increase — Wrong on both counts. The total goes down, not up, and by 0.6 on a base of 10, which is 6%, not 5%.

Concept

When the parts of a total change by different percentages, the total's change is a weighted average of the part changes, each weighted by that part's share of the total.

Food is 2⁄10, clothing 4⁄10 and entertainment 4⁄10 of spending:
0.2 × (−10) + 0.4 × (+5) + 0.4 × (−15) = −2 + 2 − 6 = −6%

Reading the ratio parts as rupee amounts gives the same answer without fractions.

Each option pairs a size (5% or 6%) with a direction, so both halves of the answer have to be right.

Key facts

A ratio 2 : 4 : 4 can be read as amounts 2, 4 and 4 out of a total of 10.
A 10% fall multiplies by 0.90, a 5% rise by 1.05 and a 15% fall by 0.85.
Percentage change = (new − old) ÷ old × 100.

Study next

Income, expenditure and savings when two of the three change by different percentagesSuccessive percentage changes on one quantity (a% then b%)Weighted averages of rates, such as average price change across items

Common traps

Adding the three rates, −10 + 5 − 15 = −20%, as if each change applied to the whole budget.
Taking a simple average, (−10 + 5 − 15) ÷ 3 ≈ −6.67%, which treats all three heads as equal.
Getting the size right and the sign wrong: the total falls, so the answer is a decrease.

Here three expense heads carry three different percentage changes. A two-part version is 25 Sep 2024, 12:30, Quant Q.19, where expenditure : savings = 4 : 1, income rises 20% and expenditure 10%, so savings rise 60%.

Related PYQs

No directly related past PYQ was found.

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