Quantitative Aptitude practice

Percentage Questions with Answers

Percentage expresses a number as a part of 100. Percentage questions in SSC CGL, CHSL and MTS, RRB NTPC and Group D, and bank prelims are everywhere, because the same idea powers profit and loss, interest, data interpretation and population problems. Typical questions ask for successive changes, comparisons between two quantities, or election and population results. Tip: learn the fraction equivalents (1/8 = 12.5%, 1/6 = 16.67%, 1/12 = 8.33%) so you can compute in your head.

Formulas you need

Percentage = (Part ÷ Whole) × 100
Percentage change = (New − Old) ÷ Old × 100
If A is x% more than B, then B is [x ÷ (100 + x)] × 100% less than A
If A is x% less than B, then B is [x ÷ (100 − x)] × 100% more than A
Successive changes of a% and b%: net change = a + b + (ab ÷ 100)
A rise of x% followed by a fall of x% gives a net fall of x²÷100 %
Final value after growth r% for n years = Original × (1 + r/100)ⁿ
Votes cast = Total voters × turnout %; valid votes = Votes cast − invalid votes
Common equivalents: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%

Worked examples

Q1. Find 35% of 480.

35% = 35/100
35 ÷ 100 × 480 = 35 × 4.8
= 168

Answer: 168

Q2. The price of an article is ₹2,500. It is increased by 20% and then reduced by 20%. Find the final price and the net percentage change.

After 20% increase: 2,500 × 1.2 = 3,000
After 20% decrease: 3,000 × 0.8 = 2,400
Net change = (2,400 − 2,500) ÷ 2,500 × 100 = −4%
Cross-check with the formula: 20² ÷ 100 = 4% fall

Answer: ₹2,400, a net fall of 4%

Q3. In an election there are 60,000 registered voters. 80% of them vote, and 5% of the votes cast are invalid. The winner gets 55% of the valid votes. By how many votes does the winner win?

Votes cast = 80% of 60,000 = 48,000
Invalid votes = 5% of 48,000 = 2,400, so valid votes = 45,600
Winner = 55% of 45,600 = 25,080
Loser = 45,600 − 25,080 = 20,520
Margin = 25,080 − 20,520 = 4,560

Answer: 4,560 votes

Shortcuts that save time

Use multipliers, not repeated percentages. A 20% rise is ×1.2 and a 20% fall is ×0.8. Chain them in one line to avoid subtraction errors.
The 'x% more, so y% less' conversion is not symmetric. Use x ÷ (100 + x). Students who flip it directly lose marks on the most common trap in this chapter.
Use the swap trick: a% of b equals b% of a. For 8% of 50 you can calculate 50% of 8 = 4 in one step.

Where this appears

SSC CGL Tier-1	Quantitative Aptitude section
SSC CHSL Tier-1	Quantitative Aptitude section
SSC MTS	Numerical and Mathematical Ability section
RRB NTPC CBT-1	Mathematics section
Bank PO/Clerk Prelims	Quantitative Aptitude section

Percentage

Practice Set

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Find 30% of 240.

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