WORD PROBLEM ON PERCENTAGE -
1) In a class, 10 % of the students failed in Maths. There are 50 students in the class. Find how many students failed in Maths. Also find the number of students who passed in Maths.
Total number of students in the class = 50 Percentage of students failed in Maths = 10 %
[To find the percentage of a given quantity, we first express the given percent as a fraction and then multiply it by the given quantity.]
.: Number of students failed in Maths =
10
------- × 50
100
[10 and 100 have the common factor 10 & 10 and 50 have the common factor 10]
= 5
[To find the number of students who passed in Maths we subtract the number of students who failed in Maths from the total number of students in the class.]
.: Number of students who passed in Maths = 50 – 5 = 45 (Ans.)
Example.2) Richa got 20 marks out of 25 in English, 31 out of 40 in Hindi and 65 out of 80 in Maths. In which subject his percentage of marks is best?
Ans.)
Marks Richa got in English = 20
Total marks in English = 25
[To express a number as percentage of another, we divide the number with the other number and then convert it into percentage by multiplying it by 100.]
20
Percentage of marks Richa got in English = ------- × 100
25
[25 and 100 have the common factor 25]
20 × 4
= ---------- = 80 %
1
Similarly,
Marks Richa got in Hindi = 31
Total marks in Hindi = 40
31
.: Percentage of marks Richa got in Hindi = ------- × 100
40
[40 and 100 have the common factor 10 & 4 and 10 have the common factor 2]
31 × 5 155
= --------- = -------- = 77.5%
2 2
Marks Rakesh got in Maths = 65
Total marks in Maths = 80
65
Percentage of marks Rakesh got in Maths = ------- × 100
80
[80 and 100 have the common factor 10 & 8 and 10 have the common factor 2]
65 × 5 325
= ----------- = -------- = 81.25 %
4 × 1 4
By comparing the percentage of marks in the three subjects we can see that 81.25 % is greater than 80 % and 77.5 %.
.: In Maths the percentage of marks of Richa is best. (Ans.)
1
Example.3) Which is greater, 0.485 or 48 ------ % ?
2
[To convert the percentage into a decimal fraction, we remove the % symbol and divide it by 100. We know that dividing by 100 means shifting the decimal point by two places to the left.]
1 (48 × 2) + 1 97
48 ------- % = --------------- % = ------- %
2 2 2
[Convert the mixed number into improper fraction]
= 48.5 %
48.5
48.5 % = -------- = 48.5 ÷ 100 = 0.485
100
1
.: We see that, 0.485 and 48 ------ % are both equal. (Ans.)
2
Example.4) In a one-day international cricket match, India scored 400 runs. Of this, Sachin Tendulkar alone had scored 156 runs. Find the percentage of runs scored by:
i) Sachin
ii) rest of the team members.
Ans.)
In the one-day international cricket match, score of Sachin Tendulkar alone = 156 runs
Total score of India = 400 runs
[To express a number as percentage of another, we divide the number with the other number and then convert it into percentage by multiplying it by 100.]
156
i) Percentage runs scored by Sachin = ------- X 100
400
[400 and 100 have the common factor 100 & 156 and 4 have the common factor 2 & 78 and 2 have the common factor 2]
39 X 1
= ----------- = = 39 %
1 X 1
[To find the score of the rest of the team members we subtract the score of Sachin Tendulkar alone from the total score of India.]
Score of rest of the team members = (400 – 156) runs = 244 runs (Ans.)
ii) Percentage of runs scored by rest of the team members =
244
= -------- X 100
400
[400 and 100 have the common factor 100 & 244 and 4 have the common factor 2 & 122 and 2 have the common factor 2]
61 × 1
= ---------- = 61 % (Ans.)
1 × 1