Percent - Grade 6 Math Questions and Problems
With Solutions and Explanations

Questions and Their Solutions

1. 
   30% of 30 =
   Solution
   30% of 30 is written as
   30% × 30 = (30 / 100) × 30 = 900 / 100 = 9
   
2. 
   150% of 60 =
   Solution
   150% of 60 is written as
   150% × 60 = (150 / 100) × 60 = (150 × 60) / 100 = 90
   
3. 
   1/4 =
   1. 4%
   2. 1%
   3. 0.25%
   4. 25%
   Solution
   We need to change the fraction 1 / 4 into a fraction with denominator 100 which is a percent
   1 / 4 = (1 × 25) / (4 × 25) = 25 / 100 = 25%
   
4. 
   0.05 =
   
   1. 50%
   2. 500%
   3. 5%
   4. 0.5%
   
   Solution
   We need to change the decimal number 0.05 into a fraction with denominator 100 which is a percent
   0.05 = 0.05 / 1 = (0.05 × 100) / (1 × 100) = 5 / 100 = 5%
   
5. 
   If 100% of a number is 15, what is 50% of the number?
   Solution
   Let n be the number
   100% of a number is 15 is written as: 100% × n = 15
   100% = 100 / 100 = 1
   Hence
   100% × n = n = 15
   We now need to find 50% of the number
   50% of 15 = (50 / 100) × 15 = 750 / 100 = 7.5
   NOTE that the above problem could be solved by noting that 50% of something is half of 100% of the same thing. Hence if 100% of something is 15 then 50% of the same thing is haflf of 15 / 2 = 7.5
   
6. 
   If 10% of a number is 7, what is 80% of the number?
   Solution
   Note that 80% of something is 8 times 10% of the same thing. Hence if 10% of a number is 7 then 80% of the same number is given by
   8 × 7 = 56
   
7. 
   Which is the greatest?
   
   1. 90% of 10
   2. 6% of 1000
   3. 5% of 1400
   4. 3% of 2500
   
   Solution
   Express as fractions with same denominator 100 and then compare
   90% of 10 = (90 / 100) × 10 = 900 / 100
   6% of 1000 = (6 / 100) × 1000 = 6000 / 100
   5% of 1400 = (5 /100) × 1400 = 7000 / 100
   3% of 2500 = (3 / 100) × 2500 = 7500 / 100
   The largest fraction is 7500 / 100 which correspond to 3% of 2500. Hence 3% of 2500 is the largest.
   
8. 
   The original price of a toy was $15. If the price is reduced by 20%, what is the new price of the toy?
   Solution
   20% of price is
   20% × 15 = $3
   The original price was $15 and was reduced by 20% or $3. Hence the new price after reduction is
   15 - 3 = $12
   
9. 
   George bought a car at $5000 and sold it at $5500. What benefit, in percent, did he make?
   
   Solution
   The benefit in dollars is
   $5500 - $5000 = $500
   Express $500 as a percent of $5000 as follows
   500 / 5000 = 5 / 50 = 10 / 100 = 10%
   
10. 
    If 20% of n is equal to 40, what is n?
    
    Solution
    "20% of n is equal to 40" is written as
    20% × n = 40
    (20 / 100) × n = 40
    Rewrite the above with fraction on the right side with denominator equal to 100
    20 n / 100 = 40 / 1 = 4000 / 100
    Since the two fractions have same denominator and are equal, their numerator must be equal. Hence
    20 n = 4000 which means that n = 200.
    
    1. 200
    2. 2000
    3. 800
    4. 80
    
    
11. 
    The price of a T-shirt was $20. It was first increased by 20%. They did not sell well the shop owner decreased the price by 20%. What is the new price of the T-shirt?
    
    1. $20
    2. $22
    3. $21
    4. $19.20
    
    
12. 
    What percent of 1 hour is 15 minutes?
    
    1. 50%
    2. 15%
    3. 75%
    4. 25%