Reverse Percentage Calculations - CCAT Test Prep

This type of question tests your understanding of finding the original value when you know a percentage of it. This skill can be useful for real-life problems, such as calculating the full price of an item when you know only a discount amount. We will solve it in a straightforward way, focusing on keeping the calculations simple and easy.

How to Find the Original Number Without Using Fractions

Question 1 - Finding the Original Number

6 is 15% of what number?

A) 20
B) 25
C) 30
D) 36
E) 40

Understand the Problem:

We know 15% of a certain number is 6.
Let’s represent that unknown number as X.

Think of 15% as a Breakdown:

15% is the same as 10% + 5%.
Our target is to determine what number gives 6 when 15% of it is taken.

Work Backwards to Find X:

First, consider what 10% would be:
If 15% of X is 6, then 10% would be a little less than 6. Let’s figure it out.
Divide 6 by 1.5 to find 10%:

6 ÷ 1.5 = 4

Now, if 10% is 4, then to get to 100%:

X = 4 × 10 = 40

Answer: 40

By breaking the percentage into smaller steps and working backwards, you can solve this problem without needing fractions.

Question 2 - Finding Original Values

12 is 20% of what number?

A) 40
B) 50
C) 60
D) 70
E) 80

Break Down 20%

20% can be thought of as 10% + 10%.

Find the Original Value:

If 20% is 12, then 10% is half of 12:

10% = 12 ÷ 2 = 6

To find 100%:

X = 6 × 10 = 60

Answer: 60

Question 3 - Finding the Whole Value

8 is 25% of what number?

A) 24
B) 28
C) 30
D) 32
E) 36

Understand 25%

25% means one-quarter of the total value.

Work Out the Total:

If 25% is 8, then to find the total value, multiply by 4:

X = 8 × 4 = 32

Answer: 32

How to Solve These Questions Easily

Break Down Percentages: Break the percentage into parts, like 10%, 20%, or 25%, to make it easier to calculate.
Work Backwards: Use the given percentage to estimate what 10% or 25% would be, then use that to find 100%.
Keep it Simple: Think of percentages as parts of the whole—use simple multiplication and division to find the original value.

This approach will help you solve these types of questions with ease.

20 Practice Questions - Finding the Original Number

10 is 25% of what number?

A) 20
B) 30
C) 40
D) 50
E) 60

15 is 30% of what number?

A) 40
B) 45
C) 50
D) 55
E) 60

18 is 20% of what number?

A) 80
B) 85
C) 90
D) 95
E) 100

9 is 15% of what number?

A) 40
B) 50
C) 55
D) 60
E) 65

5 is 10% of what number?

A) 40
B) 45
C) 50
D) 55
E) 60

14 is 25% of what number?

A) 42
B) 48
C) 56
D) 60
E) 64

16 is 20% of what number?

A) 60
B) 70
C) 80
D) 90
E) 100

24 is 40% of what number?

A) 50
B) 55
C) 60
D) 65
E) 70

30 is 50% of what number?

A) 40
B) 50
C) 60
D) 70
E) 80

6 is 12% of what number?

A) 40
B) 45
C) 50
D) 55
E) 60

12 is 15% of what number?

A) 60
B) 70
C) 80
D) 90
E) 100

20 is 25% of what number?

A) 70
B) 75
C) 80
D) 85
E) 90

25 is 20% of what number?

A) 110
B) 120
C) 125
D) 130
E) 140

21 is 30% of what number?

A) 60
B) 65
C) 70
D) 75
E) 80

28 is 35% of what number?

A) 70
B) 75
C) 80
D) 85
E) 90

18 is 20% of what number?

A) 80
B) 85
C) 90
D) 95
E) 100

32 is 40% of what number?

A) 70
B) 75
C) 80
D) 85
E) 90

36 is 45% of what number?

A) 70
B) 75
C) 80
D) 85
E) 90

8 is 10% of what number?

A) 60
B) 70
C) 80
D) 90
E) 100

27 is 15% of what number?

A) 160
B) 170
C) 180
D) 190
E) 200

Answers

C) 40
B) 50
E) 90
D) 60
C) 50
C) 56
C) 80
C) 60
C) 60
C) 50
D) 80
C) 80
C) 125
C) 70
C) 80
C) 90
C) 80
C) 80
C) 80
C) 180

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