Percentage Word Problem// Math // Fractions to Percentages//Percentage to Decimal

Percentage Word Problem

Percentages are useful in conveying information in everyday life. The symbol, % is used to represent 'percent'.

Thus 50 %  is read as '50 percent.

Suppose the sales of a company last year were $ 100 million and the sales of the company this year are $200 million. The sales of the company this year are 200/100  =  200% of its sales last year.

Expressing a Percentage as a Fraction:

a) Express each of the following percentages as a fraction.

i) 88%

= 88/100

= 22/25

ii) 128 %

= 128 /100

=  32/25

iii) 0.5%

= 0.5/100

= 1/200

b) Express each of the following fractions as a percentage.

i)  1/2

=  1/2   X    100%

=   50%

ii)  9/8

=   9/8   X  100%

=  900/8 %

=  112.5 %

a) Express each of the following percentages as a fraction.

i)  45 %

=  45/100

= 9/20

b) Express each of the following fractions as a percentage.

i) 17/20

=  17 / 20  X100

= 85 %

Q.2. Express each of the following percentages as a decimal.

i) 85%

= 85 / 100

= 0.85

Express each of the following decimals as a percentage.

i) 0.16

= 0.16 X 100%

= 16%

Q.1. A class has 40 students. Given that 75% of them passed a Mathematics​ test. Calculate the number of students who failed the test. 

Solution: 

Percentage​ of students who failed the test = 100% - 75 %
                                                                  = 25%
 Number of students who failed the test = 25% x 40 
                                                                 = 0.25 x 40
                                                               = 10 Ans.

2. A school has 1500 students. Given that 3% of them were late for school on a particular day, find the number of students who were punctual for school. 

Solution:

Number of students who are late for school = 3% of 1500 

                                                               = 3/100 x 1500 

                                                               =

 Number of students who are punctual for school = 1500 – 45 

                                                                        = 

 Q.3. 1800 people attended the National Day dinner in a certain constituency. Given that 35.5% of them were men, 40% of them were women and the rest were children, find the number of children who attended the dinner.

Solution:

Number of men = 35.5/100 x 1800 

                            = 639 

Number of women = 40/100 x 1800 

                               = 720 

Total number of men and women = (639 + 720) 

                                                       = 1359 

                 Number of children    = 1800 – 1359 

Q.4. In 2011, 600 out of 1600 people passed the entrance test of a school. 400 out of 1000 people passed the entrance test of the same school in 2012. In which year did a higher percentage​ of people pass the entrance test of the school?

 Percentage​ of people who passed the entrance​ test​ in 2011 = 600/1600 x 100% 

Percentage of people who passed the entrance test in 2012 = 400/1000 x 100% 

A higher percentage of people passed the entrance test of the school in 2012. 

Q.5. There were 30,000 people in city A and 4000 people attended its New year party. There were 25,000 people in city B and 2800 people attended its New Year party. Which city had a higher percentage of people attending its party?

 Percentage of people who attended party in city A = 4,000/30,000 x 100 

Percentage of people who attended party in city B = 2800/25,000 x 100 

 A higher percentage of people attended its party in city A

 

 

Conversions Involving Percentages:

iv) Converting Percentage to Decimal numbers: 

Represent 60% as a decimal number 60 %     = 60 out of 100 
                                                                         = 60/100
                                                                         = 6/10
                                                                       = 0.6 

iii) Converting Percentage to Fractions: 

Represent 38% as a fraction. 38 %      = 38 out of 100
                                                             = 38/100 
                                                            = 19/50 

ii) Converting Decimal Numbers to Percentages: 

a) Represent 0.63 as a percentage. 

Conversions Involving Percentages: Fractions to Percentages
Represent ¾ as a percentage.

Percentage Word Problem: 

Q1. Rama bought a pen for $5. If she had $20 in her pocket, what percentage of the money did she spend on the pen? 

Solution:

Money spent by Rama = $5 out of $20 = 5/20 x 100 

                                     = 25 % 

Ans: 25%

Q2. 40% of 1 kg is how many grams?

Solution: 

1 kg = 1000 g 

40% of 1000 g = 40/100 x 1000 = 400 gm

Ans: 400gm

Q3. A tank had 80 L of water. 20% of the water was drained out. How many litres of water remained in the tank?

Solution: 

Water drained out = 20% of 80 L = 20/100 x 80 = 16 L 

Water left in the tank = 80L - 16 L = 64 L

Ans: 64L

Q4. Monica runs 100 m in 12 seconds. Kanika takes 5% more time to run 100m. 
How much time does Kanika take?

 Solution: 

5% of 12 seconds = 5/100 x 12 = 0.6 Seconds

Time taken by Kanika = 12 + 0.6 = 12.6 seconds

Ans: 12.6seconds.