Grade 6 Percent Questions with Step-by-Step Solutions and Explanations

Questions and Their Solutions

1. 
   \[ 30\% \; \text{of} \; 30 = \]

   Solution

   \( 30\% \; \text{of} \; 30 \) is written as \[ 30\% \times 30 = \dfrac{30}{100} \times 30 = \dfrac{900}{100} = 9 \]
2. 
   \[ 150\% of 60 = \]

   Solution

   \( 150\% of 60 \) is written as \( 150\% \times 60 = \dfrac{150}{100} \times 60 = \dfrac{150 \times 60}{100} = 90 \)
   
3. 
   \[ \dfrac{1}{4} = \]
   1. 4%
   2. 1%
   3. 0.25%
   4. 25%

   Solution

   
   We need to change the fraction \( \dfrac{1}{4} \) into a fraction with denominator 100 which is a percent \[ \dfrac{1}{4} = \dfrac{1 \times 25}{4 \times 25} = \dfrac{25}{100} = 25\% \]
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 \[ 0.05 = \dfrac{0.05}{1} = \dfrac{0.05 \times 100}{1 \times 100} = \dfrac{5}{100} = 5\% \]
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: \[ 100\% \times n = 15 \] Since \( 100\% = \dfrac{100}{100} = 1 \), we have: \[ n = 15 \] Now find 50% of the number: \[ 50\% \times 15 = \dfrac{50}{100} \times 15 = \dfrac{750}{100} = 7.5 \] NOTE: 50% of something is half of 100%. Hence, \( \dfrac{15}{2} = 7.5 \)
   
6. 
   If 10% of a number is 7, what is 80% of the number?

   Solution

   Note that 80% is 8 times 10%. Hence: \[ 8 \times 7 = 56 \]
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:
   \( 90\% \times 10 = \dfrac{90}{100} \times 10 = \dfrac{900}{100} \)
   \( 6\% \times 1000 = \dfrac{6}{100} \times 1000 = \dfrac{6000}{100} \)
   \( 5\% \times 1400 = \dfrac{5}{100} \times 1400 = \dfrac{7000}{100} \)
   \( 3\% \times 2500 = \dfrac{3}{100} \times 2500 = \dfrac{7500}{100} \)
   The largest is \( \dfrac{7500}{100} \). Hence, 3% of 2500 is the greatest.
   
8. 
   The original price of a toy was $15. If the price is reduced by 20%, what is the new price?

   Solution

   20% of 15 is: \[ 20\% \times 15 = \dfrac{20}{100} \times 15 = 3 \] New price: \( 15 - 3 = 12 \)
   
9. 
   George bought a car at $5000 and sold it at $5500. What benefit, in percent, did he make?

   Solution

   Benefit in dollars: \[ 5500 - 5000 = 500 \] Express as percent: \[ \dfrac{500}{5000} = \dfrac{10}{100} = 10\% \]
   
10. 
    If 20% of n is equal to 40, what is n?

    Solution

    \[ 20\% \times n = 40 \] Whivh may be written as \[ \dfrac{20}{100} \times n = 40 \] and \[ \dfrac{20n}{100} = \dfrac{4000}{100} \] So, \( 20n = 4000 \implies n = 200 \)
11. 
    The price of a T-shirt was $20. It was first increased by 20%. Then decreased by 20%. What is the new price?
    

    Solution

    
    First increase the price by 20%: \[ 20\% \times 20 = \dfrac{20}{100} \times 20 = 4 \] New price after increase: \[ 20 + 4 = 24 \] Now decrease the new price by 20%: \[ 20\% \times 24 = \dfrac{20}{100} \times 24 = 4.8 \] New price after decrease: \[ 24 - 4.8 = 19.2 \] Therefore, the new price of the T-shirt is: \[ \$19.20 \]
12. 
    What percent of 1 hour is 15 minutes?
    
    1. 50%
    2. 15%
    3. 75%
    4. 25%

Solution