Percentage of Percentage - CCAT Test Prep

This type of question tests your understanding of calculating percentages in a sequential way, helping you determine a percentage of a percentage in a series of simple steps. You may encounter this type of question in real-life scenarios, such as finding discounts on items or working with nested percentages for budgeting purposes. To solve it effectively, break down each calculation into smaller, easily manageable parts.

sequential-percentages

How to Solve Sequential Percentage Calculations Step-by-Step

Question 1 - Nested Percentage Calculation

What is 60% of 75% of 60?

  • A) 21
  • B) 27
  • C) 30
  • D) 35
  • E) 42

Step-by-Step Solution:

To solve this, follow these easy steps:

  1. Calculate 75% of 60:
    • 75% can be thought of as three-quarters.
    • First, divide 60 by 4 to get one-quarter:
    60 ÷ 4 = 15
    • Multiply 15 by 3 to get three-quarters:
    15 × 3 = 45
    • So, 75% of 60 is 45.
  2. Calculate 60% of the Result:
    • Now, we need 60% of 45.
    • Think of 60% as slightly more than half. Start by finding 50% of 45:
    45 ÷ 2 = 22.5
    • 60% is 10% more than half, so we need to find 10% of 45:
    10% of 45 
    = 45 ÷ 10 
    = 4.5
    • Add 22.5 and 4.5 to get 60% of 45:
    22.5 + 4.5 = 27

Answer: 27

This approach makes it easy to handle percentages step by step, allowing you to do calculations quickly without complicated multiplications.

Question 2 - Percentage of Percentage

What is 80% of 50% of 100?

  • A) 30
  • B) 40
  • C) 50
  • D) 60
  • E) 80

Step-by-Step Solution:

  1. Calculate 50% of 100:
    • 50% is the same as half:
    50% of 100 
    = 100 ÷ 2 
    = 50
  2. Calculate 80% of the Result:
    • Think of 80% as four-fifths.
    • First, find one-fifth of 50:
    50 ÷ 5 = 10
    • Multiply 10 by 4 to get four-fifths:
    10 × 4 = 40

Answer: 40

Question 3 - Percentages in Series

What is 25% of 40% of 80?

  • A) 8
  • B) 10
  • C) 12
  • D) 16
  • E) 20

Step-by-Step Solution:

Calculate 40% of 80:

  • Think of 40% as two-fifths.
  • First, find one-fifth of 80:
80 ÷ 5 = 16
  • Multiply 16 by 2:
16 × 2 = 32

Calculate 25% of the Result:

  • 25% is one-quarter of 32:
32 ÷ 4 = 8

Answer: 8

How to Solve These Questions in Your Head

  1. Break Down Percentages into Simple Fractions: Convert percentages into easy fractions. For example, 50% is 1/2, 75% is 3/4, 25% is 1/4.
  2. Perform Simple Multiplications or Divisions: Start by applying one percentage, then the next. Use round numbers or small fractions to make calculations easier.
  3. Work Step by Step: Focus on each percentage independently before moving to the next, so you avoid confusion.

By simplifying each calculation and breaking it down into smaller parts, you can solve percentage problems quickly in your head.

20 Practice Questions - Sequential Percentage Calculations

  1. What is 50% of 30% of 200?
  • A) 15
  • B) 20
  • C) 25
  • D) 30
  • E) 35
  1. What is 60% of 40% of 90?
  • A) 18
  • B) 20
  • C) 21
  • D) 22
  • E) 24
  1. What is 70% of 50% of 60?
  • A) 15
  • B) 18
  • C) 21
  • D) 24
  • E) 28
  1. What is 30% of 75% of 80?
  • A) 18
  • B) 22
  • C) 24
  • D) 26
  • E) 28
  1. What is 80% of 25% of 200?
  • A) 30
  • B) 35
  • C) 40
  • D) 45
  • E) 50
  1. What is 90% of 50% of 100?
  • A) 30
  • B) 40
  • C) 45
  • D) 50
  • E) 55
  1. What is 25% of 60% of 120?
  • A) 12
  • B) 15
  • C) 18
  • D) 20
  • E) 22
  1. What is 40% of 80% of 150?
  • A) 36
  • B) 45
  • C) 48
  • D) 50
  • E) 60
  1. What is 75% of 25% of 80?
  • A) 12
  • B) 15
  • C) 18
  • D) 20
  • E) 25
  1. What is 20% of 90% of 50?
  • A) 5
  • B) 7
  • C) 9
  • D) 10
  • E) 15
  1. What is 30% of 70% of 100?
  • A) 15
  • B) 20
  • C) 21
  • D) 24
  • E) 28
  1. What is 25% of 80% of 40?
  • A) 6
  • B) 8
  • C) 10
  • D) 12
  • E) 14
  1. What is 50% of 60% of 90?
  • A) 22
  • B) 24
  • C) 25
  • D) 27
  • E) 30
  1. What is 35% of 40% of 200?
  • A) 20
  • B) 28
  • C) 35
  • D) 40
  • E) 42
  1. What is 45% of 25% of 160?
  • A) 16
  • B) 18
  • C) 20
  • D) 25
  • E) 28
  1. What is 70% of 90% of 70?
  • A) 35
  • B) 40
  • C) 44
  • D) 49
  • E) 50
  1. What is 25% of 50% of 120?
  • A) 10
  • B) 12
  • C) 15
  • D) 20
  • E) 25
  1. What is 60% of 75% of 80?
  • A) 24
  • B) 30
  • C) 36
  • D) 40
  • E) 45
  1. What is 80% of 60% of 150?
  • A) 54
  • B) 60
  • C) 64
  • D) 72
  • E) 80
  1. What is 50% of 25% of 200?
  • A) 15
  • B) 20
  • C) 22
  • D) 25
  • E) 30

Answers

  1. A) 30.0
  2. C) 21.6
  3. C) 21.0
  4. A) 18.0
  5. C) 40.0
  6. C) 45.0
  7. C) 18.0
  8. C) 48.0
  9. A) 15.0
  10. C) 9.0
  11. C) 21.0
  12. B) 8.0
  13. D) 27.0
  14. B) 28.0
  15. A) 18.0
  16. D) 44.1
  17. A) 15.0
  18. C) 36.0
  19. D) 72.0
  20. D) 25.0
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