CCAT Percentages and Ratios: Fast Methods & Examples
Percentage and ratio questions reward candidates who can recognize relationships quickly and calculate without a calculator.
Common independent CCAT practice formats include:
- finding a percentage of a quantity;
- percentage increase or decrease;
- finding an original value;
- comparing percentages;
- scaling ratios;
- dividing a total in a ratio;
- solving proportions.
Criteria officially groups this work within Math and Logic and does not guarantee one fixed number of percentage or ratio questions.
Practice timed CCAT numerical questions
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Use our CCAT practice comparison and online tests first, or take the free 30-question CCAT practice test. For an external numerical guide, review JobTestPrep's CCAT math questions. Its complete CCAT PrepPack is another independent option.
Scope and Official Context
This page focuses on percentage and ratio methods. Criteria confirms that the CCAT includes math and logic questions but does not publish a permanent subtype allocation for every candidate.
Criteria’s current candidate guidance confirms 50 questions in 15 minutes, no calculator, no additional penalty for an incorrect answer, and advice to guess and move on when a question consumes too much time.
Essential Percentage Relationships
Memorize useful equivalents:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
These relationships reduce calculation time.
Find a Percentage of a Number
Use:
percentage × quantity
Example:
15% of 260
Split 15% into 10% and 5%:
10% of 260 = 26
5% of 260 = 13
26 + 13 = 39
Answer: 39.
Use 1% as a Building Block
Example:
17% of 300
1% of 300 = 3
17% = 17 × 3 = 51
Answer: 51.
This is useful when the percentage is not a common fraction.
Percentage Increase
Use:
increase ÷ original value × 100
Example:
A price rises from £120 to £150.
Increase:
150 - 120 = 30
Percentage increase:
30 ÷ 120 = 0.25 = 25%
Answer: 25%.
Always divide by the original value.
Percentage Decrease
Example:
A value falls from 250 to 200.
Decrease:
250 - 200 = 50
Percentage decrease:
50 ÷ 250 = 0.20 = 20%
Answer: 20%.
Apply a Percentage Increase Directly
A 20% increase means the new value is 120% of the original:
original × 1.20
Example:
80 × 1.20 = 96
Apply a Percentage Decrease Directly
A 15% decrease leaves 85%:
original × 0.85
Example:
200 × 0.85 = 170
Reverse Percentages
Example:
After a 25% increase, a value is 100. What was the original?
The final value represents 125%:
100 ÷ 1.25 = 80
Answer: 80.
A fast answer-choice check is:
25% of 80 = 20
80 + 20 = 100
Successive Percentage Changes
A 10% increase followed by a 10% decrease does not return to the original value.
Start with 100:
100 × 1.10 = 110
110 × 0.90 = 99
The final value is 1% below the original.
Do not add percentage changes mechanically when the base changes.
Ratio Basics
A ratio of:
3:5
means that for every 3 units of the first quantity, there are 5 units of the second.
Order matters.
If the ratio is analysts to managers, 3:5 is not interchangeable with 5:3.
Scale a Ratio
Example:
The ratio of analysts to managers is 3:5. There are 20 managers. How many analysts?
The manager side changed from 5 to 20:
20 ÷ 5 = 4
Apply the same factor:
3 × 4 = 12
Answer: 12.
Divide a Total in a Ratio
Example:
Red and blue items are in the ratio 7:4. There are 44 items in total. How many are red?
Total parts:
7 + 4 = 11
Value of one part:
44 ÷ 11 = 4
Red items:
7 × 4 = 28
Answer: 28.
Three-Part Ratios
Example:
A total of 72 tasks is divided among A, B, and C in the ratio 2:3:4. How many tasks go to C?
Total parts:
2 + 3 + 4 = 9
One part:
72 ÷ 9 = 8
C receives:
4 × 8 = 32
Answer: 32.
Proportions
Example:
4/7 = x/35
Since 7 becomes 35 by multiplying by 5:
x = 4 × 5 = 20
Answer: 20.
Use scaling before cross-multiplication when the factor is obvious.
Ratio to Percentage
Example:
The ratio of completed to incomplete tasks is 3:2. What percentage are complete?
Total parts:
3 + 2 = 5
Completed fraction:
3/5 = 60%
Answer: 60%.
Percentage to Ratio
Example:
40% of a group is remote and 60% is office-based. What is the ratio remote to office-based?
40:60
Simplify by 20:
2:3
Answer: 2:3.
Weighted Percentage Problems
Example:
A £120 item is discounted by 25%, and an £80 item is discounted by 10%. What percentage is saved across the combined original cost?
Savings:
25% of 120 = 30
10% of 80 = 8
Total saving = 38
Original total:
120 + 80 = 200
Overall percentage saved:
38 ÷ 200 = 19%
Answer: 19%.
Do not average 25% and 10% because the original prices differ.
Fast Mental Methods
Find 5%
Find 10%, then halve it.
Find 15%
Add 10% and 5%.
Find 25%
Divide by 4.
Find 75%
Find three quarters or subtract 25%.
Find 12.5%
Divide by 8.
See the CCAT mental-math guide for more techniques.
Common Traps
- Using the final value as the percentage-change base.
- Reversing ratio labels.
- Forgetting to add ratio parts before dividing a total.
- Treating successive percentage changes as simple addition.
- Averaging percentages without considering different base quantities.
- Moving a decimal in the wrong direction.
- Using a calculator during realistic practice.
Timed Strategy
- identify whether the question asks for a quantity, percentage, original value, or ratio part;
- label the ratio order;
- use common percentage equivalents;
- estimate the answer range;
- simplify before multiplying;
- use answer choices when reverse calculation is faster;
- guess and continue when the setup remains unclear.
Original Practice Examples
Example 1
35% of 180 = ?
30% = 54
5% = 9
Total = 63
Answer: 63.
Example 2
A quantity decreases from 160 to 136. What is the percentage decrease?
24 ÷ 160 = 15%
Answer: 15%.
Example 3
The ratio of X to Y is 4:7. If X is 20, what is Y?
Scale factor:
20 ÷ 4 = 5
7 × 5 = 35
Answer: 35.
Practice before test day
Start with the free CCAT practice test, the CCAT math practice and the complete preparation guide. For a full timed simulation, use the free and premium CCAT practice tests or the CCAT study plan. Structured preparation is also available through CCATPracticeTest.com practice options and the JobTestPrep CCAT PrepPack.
Frequently Asked Questions
Are percentages and ratios guaranteed on every CCAT?
Criteria does not publish one fixed narrow subtype distribution. They remain central calculator-free numerical skills for preparation.
Can I use a calculator?
No. The standard CCAT does not permit calculators.
What is the most common percentage-change mistake?
Dividing the change by the final value instead of the original value.
What is the most common ratio mistake?
Reversing the labels or forgetting to total the ratio parts.
Where can I practice more?
Use the CCAT word-problems guide and CCAT math practice.
As a secondary independent option, compare JobTestPrep’s Criteria CCAT preparation.
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