Percentage Reduction Questions : CCAT Test Prep

This type of question is all about understanding price reductions and how they affect the total cost. The main idea is to figure out the average cost of an item by dividing the total cost by the number of items. Once you have the average price, the question asks you to reduce that price by a certain percentage. This simulates real-life situations, like getting a discount on a product. After calculating the reduced price, you then multiply it by the number of items to get the new total cost. These questions test your ability to handle basic math, especially when it comes to percentages and averages. It’s a practical way to check how you deal with numbers in everyday situations.

How to Solve Percentage Reduction Questions Easily?

Question 1

If the total cost of 6 books is $48, and the average price per book is reduced by 25%, how much will the 6 books cost at the new rate?

A) $30
B) $32
C) $34
D) $36
E) $38

Step-by-Step Solution:

To find the average price per book:


Average price 
	= Total cost ÷ Number of books

Average price 
	= 48 ÷ 6 
	= 8

Now, calculate the price reduction. Since the price is reduced by 25%, and 25% is the same as one-quarter:


Price reduction 
	= 8 ÷ 4 
	= 2

The new price per book is:


New price 
	= Original price - Reduction
New price 
	= 8 - 2 
	= 6

Finally, calculate the total cost at the new rate:


Total cost 
	= New price × Number of books

Total cost 
	= 6 × 6 
	= 36

Answer: $36

Question 2

If the total cost of 10 markers is $75, and the average price per marker is reduced by 30%, how much will the 10 markers cost at the new rate?

A) $45
B) $50
C) $52.50
D) $55
E) $60

Step-by-Step Solution:

To find the average price per marker:


Average price 
	= Total cost ÷ Number of markers

Average price 
	= 75 ÷ 10 
	= 7.50

Now, calculate the price reduction. Since the price is reduced by 30%, you can find 30% of $7.50:


Price reduction 
	= 30% of 7.50

Price reduction 
	= 0.30 × 7.50 
	= 2.25

The new price per marker is:


New price 
	= Original price - Reduction

New price 
	= 7.50 - 2.25 
	= 5.25

Finally, calculate the total cost at the new rate:


Total cost 
	= New price × Number of markers

Total cost 
	= 5.25 × 10 
	= 52.50

Answer: $52.50

Question 3

If the total cost of 4 shoes is $320, and the average price per shoe is reduced by 15%, how much will the 4 shoes cost at the new rate?

A) $240
B) $250
C) $260
D) $270
E) $280

Step-by-Step Solution:

To find the average price per shoe:


Average price 
	= Total cost ÷ Number of shoes

Average price 
	= 320 ÷ 4 
	= 80

Now, calculate the price reduction. Since the price is reduced by 15%, you can find 15% of $80:


Price reduction 
	= 15% of 80

Price reduction 
	= 0.15 × 80 
	= 12

The new price per shoe is:


New price 
	= Original price - Reduction

New price 
	= 80 - 12 
	= 68

Finally, calculate the total cost at the new rate:


Total cost 
	= New price × Number of shoes

Total cost 
	= 68 × 4 
	= 272

Answer: $272

How to Solve These Questions in Your Head

Start with the total cost and number of items to find the original price per item (divide total cost by number of items).
Calculate the percentage reduction by multiplying the original price by the percentage (e.g., 20% is the same as multiplying by 0.2).
Subtract the reduction from the original price to get the new price per item.
Multiply the new price by the number of items to find the total cost at the new rate.

This method helps you solve problems step by step without needing to write everything down. Breaking the problem into smaller chunks makes it easier to do the math in your head.

Here are 20 practice questions with options, followed by the answers at the end.

20 Practice Questions

If the total cost of 8 pens is $24, and the average price per pen is reduced by 10%, how much will the 8 pens cost at the new rate?

A) $16
B) $17.28
C) $18
D) $19.20
E) $20

If the total cost of 5 books is $40, and the average price per book is reduced by 20%, how much will the 5 books cost at the new rate?

A) $30
B) $32
C) $34
D) $35
E) $36

If the total cost of 4 shirts is $80, and the average price per shirt is reduced by 25%, how much will the 4 shirts cost at the new rate?

A) $45
B) $50
C) $60
D) $65
E) $70

If the total cost of 7 mugs is $42, and the average price per mug is reduced by 15%, how much will the 7 mugs cost at the new rate?

A) $30.87
B) $31.92
C) $34.65
D) $35.70
E) $36

If the total cost of 3 dresses is $150, and the average price per dress is reduced by 20%, how much will the 3 dresses cost at the new rate?

A) $100
B) $110
C) $120
D) $130
E) $135

If the total cost of 10 candles is $50, and the average price per candle is reduced by 15%, how much will the 10 candles cost at the new rate?

A) $37.50
B) $40
C) $42.50
D) $45
E) $46

If the total cost of 6 hats is $90, and the average price per hat is reduced by 30%, how much will the 6 hats cost at the new rate?

A) $54
B) $57
C) $60
D) $63
E) $66

If the total cost of 9 pairs of socks is $72, and the average price per pair is reduced by 25%, how much will the 9 pairs of socks cost at the new rate?

A) $40.50
B) $48
C) $54
D) $60
E) $62

If the total cost of 5 jackets is $250, and the average price per jacket is reduced by 10%, how much will the 5 jackets cost at the new rate?

A) $200
B) $210
C) $220
D) $225
E) $230

If the total cost of 12 notebooks is $36, and the average price per notebook is reduced by 10%, how much will the 12 notebooks cost at the new rate?

A) $28.80
B) $30.60
C) $32.40
D) $33.60
E) $34.80

If the total cost of 4 plates is $48, and the average price per plate is reduced by 20%, how much will the 4 plates cost at the new rate?

A) $28
B) $30
C) $32
D) $36
E) $38

If the total cost of 3 pairs of shoes is $270, and the average price per pair is reduced by 25%, how much will the 3 pairs of shoes cost at the new rate?

A) $175
B) $180
C) $195
D) $200
E) $210

If the total cost of 8 shirts is $160, and the average price per shirt is reduced by 20%, how much will the 8 shirts cost at the new rate?

A) $96
B) $102
C) $110
D) $120
E) $128

If the total cost of 9 scarves is $135, and the average price per scarf is reduced by 15%, how much will the 9 scarves cost at the new rate?

A) $99
B) $102
C) $108
D) $112
E) $115

If the total cost of 5 belts is $75, and the average price per belt is reduced by 10%, how much will the 5 belts cost at the new rate?

A) $60
B) $62.50
C) $65
D) $67.50
E) $70

If the total cost of 7 ties is $140, and the average price per tie is reduced by 25%, how much will the 7 ties cost at the new rate?

A) $73.50
B) $78.75
C) $85
D) $91.25
E) $96.25

If the total cost of 10 plates is $120, and the average price per plate is reduced by 20%, how much will the 10 plates cost at the new rate?

A) $88
B) $90
C) $92
D) $96
E) $100

If the total cost of 6 glasses is $48, and the average price per glass is reduced by 15%, how much will the 6 glasses cost at the new rate?

A) $36.72
B) $38.88
C) $40
D) $41.04
E) $42.12

If the total cost of 2 phones is $1,200, and the average price per phone is reduced by 20%, how much will the 2 phones cost at the new rate?

A) $960
B) $980
C) $1,000
D) $1,040
E) $1,080

If the total cost of 10 bags is $500, and the average price per bag is reduced by 15%, how much will the 10 bags cost at the new rate?

A) $375
B) $400
C) $425
D) $450
E) $475

Answers

B) $17.28
A) $30
C) $60
B) $31.92
C) $120
A) $37.50
A) $54
C) $54
D) $225
C) $32.40
C) $32
C) $195
D) $120
C) $108
B) $67.50
B) $78.75
D) $96
B) $38.88
A) $960
B) $400

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