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Percentage — Concept & Conversions

Quantitative Aptitude · Percentage

Useful for: SSC CGL

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Overview

Percentage means "per hundred"; fast fraction–percentage conversion and base-change logic solve most items.

Key points

x% of y = y% of x (e.g. 8% of 50 = 50% of 8 = 4).
Key conversions: 1/8 = 12.5%, 1/6 = 16.67%, 1/7 ≈ 14.29%, 1/9 = 11.11%, 1/11 = 9.09%, 1/12 = 8.33%.
If A is r% more than B, B is r/(100 + r) × 100% less than A.
If price rises by r%, consumption must fall by r/(100 + r) × 100% to keep expenditure unchanged.
Percentage change = (change ÷ original) × 100.

Explanation

Always identify the base: "more than B" means B is the base.
Percentage points differ from percent: 10% to 12% is a rise of 2 percentage points but 20%.
In elections: votes for winner − loser = given margin; set up the equation on total valid votes.
Use fraction equivalents to avoid long multiplication.

Step by step

Find the base.
Convert % to a fraction.
Compute and check that the result is reasonable.

Examples

40% of 250 = 2/5 × 250 = 100.
A’s salary is 20% more than B’s. B’s salary is less than A’s by 20/120 × 100 = 16.67%.
Price of sugar rises 25%. To keep spending the same, consumption must fall by 25/125 × 100 = 20%.

Traps and advanced points

Trap: Using the wrong base (answering 20% instead of 16.67% above).
Trap: Adding percentages of different bases directly.
Trap: Confusing percentage points with percent change.

Quick revision

r% more ↔ r/(100+r) less.
Learn 1/2 to 1/12 as percentages.
Base = "than ___".

Practice MCQs

If 30% of a number is 135, what is 80% of that number?
1. 300
2. 400
3. 360
4. 450
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Answer: (c) 360. 30% = 135 → 1% = 4.5 → number = 450.
Two successive discounts of 20% and 10% are equivalent to a single discount of:
1. 28%
2. 30%
3. 32%
4. 25%
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Answer: (a) 28%. Successive discount formula: a+b-ab/100 = 20+10-(20×10)/100 = 30-2 = 28%.
If A's salary is 25% more than B's, then B's salary is less than A's by:
1. 20%
2. 25%
3. 15%
4. 30%
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Answer: (a) 20%. Trick formula: x/(100+x) × 100 = 25/125 × 100 = 20%.
In an election between two candidates, the winner got 60% votes and won by 24000 votes. Total valid votes were:
1. 150000
2. 90000
3. 120000
4. 100000
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Answer: (c) 120000. Winner 60%, loser 40%.
The population of a town increases by 10% in the first year and decreases by 10% in the second. Net change over two years is:
1. 1% decrease
2. No change
3. 1% increase
4. 2% decrease
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Answer: (a) 1% decrease. Successive: +10, -10 → 10+(-10)+(10×-10)/100 = 0-1 = -1%.
If the price of sugar rises by 25%, by how much percent must a family reduce consumption to keep expenditure the same?
1. 30%
2. 20%
3. 25%
4. 15%
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Answer: (b) 20%. Formula: x/(100+x) × 100 = 25/125 × 100 = 20%.
45% of 280 + 28% of 450 = ?
1. 245
2. 252
3. 240
4. 260
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Answer: (b) 252. 45% of 280 = 126.
A student scored 30% and failed by 45 marks. Another scored 42% and got 27 marks more than passing. Passing marks are:
1. 220
2. 240
3. 210
4. 225
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Answer: (d) 225. Maano total = T.
If 60% of students passed and 240 failed, the total number of students is:
1. 500
2. 400
3. 720
4. 600
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Answer: (d) 600. Failed = 40% = 240.
The value of a machine depreciates by 10% every year. If its present value is Rs 72900, its value 3 years hence will be:
1. Rs 52000
2. Rs 53144.10
3. Rs 51000
4. Rs 54000
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Answer: (b) Rs 53144.10. Depreciation: value × (1 - 10/100)^3 = 72900 × (0.9)^3 = 72900 × 0.729 = 53144.10 Rs.
15% of a number is 510. What is the number?
1. 3740
2. 4080
3. 3060
4. 3400
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Answer: (d) 3400. Number = 510×100/15.
40% of a number is 652. What is the number?
1. 1467
2. 1956
3. 1793
4. 1630
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Answer: (d) 1630. Number = 652×100/40.
25% of a number is 248. What is the number?
1. 992
2. 1091.2
3. 892.8
4. 1190.4
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Answer: (a) 992. Number = 248×100/25.
40% of a number is 412. What is the number?
1. 1030
2. 1236
3. 927
4. 1133
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Answer: (a) 1030. Number = 412×100/40.
30% of a number is 753. What is the number?
1. 3012
2. 2761
3. 2510
4. 2259
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Answer: (c) 2510. Number = 753×100/30.