Percentage Questions for Class 8 with answers
Percentage
* Convert a Percentage into a Fraction
Rule : For converting a percentage into a fraction, divide it by 100 and remove the sign %,
Thus x% = x/100.
Convert each of the following into a fraction :
i) 68% = 68 / 100 = 17 / 25
ii) 3 1/3% = 10/3 % = 10/300 = 1/30
iii) 224 % = 224/100 = 56/25
iv) 0.05 % = 0.05 /100 = 5 /10000 = 1 / 2000
* Convert a Fraction into a Percentage
Rule : For converting fraction into a percentage, multiply the fraction by 100 and put the sign % .
Convert each of the following into a percentage:
i) 2/15 = (2/15 * 100 ) % = 200 /15 % = 40/3 %
ii) 9/40 = (9 /40 * 100) % = 900 / 40 = 90 / 4 % = 45 / 2 %
iii) 1 2/3 = 5 / 3 = (5/3 * 100) % = 500/3 %
iv) 2 2/5 = 12/5 = (12/5 * 100 ) % = 1200/5 % = 240%
* Convert a Percentage into a Ratio
Rule : To convert a percentage into a ratio, first convert the given percentage into a fraction in the simplest form and then express it as a ratio.
Express each of the following as a ratio .
i) 48% = 48 / 100 = 12 / 25 = 12 : 25
ii) 26 2/3 % = 80 / 3 % = 80 / 300 = 8 /30 = 4 / 15 = 4 : 15
iii) 0.06 % = 0.06 / 100 = 6 / 10000 = 3 / 5000 = 3 : 5000
iv) 120% = 120 / 100 = 12 / 10 = 6 / 5 = 6 : 5
* Convert a ration into a Percentage
Rule : First write ratio as fraction and then multiply the fraction by 100 and put the sign %
Express each of following rations as a percentage .
i) 13 : 20 = 13 / 20 = ( 13/ 20 * 100 ) % = 1300 / 20 % = 65 %
ii) 11 : 18 = 11/ 18 = ( 11/ 18 * 100) % = 1100 / 18 % = 550 / 9 %
iii) 87 : 25 = 87 / 25 = ( 87 /25 * 100 ) % = 8700 / 25 = 348 %
* Convert a Decimal into a Percentage
Rule : First convert the given decimal into a fraction and then multiply the fraction by 100 and put the sign %
Express each of the following decimal as a Percentage
i) 0.2 = 2 /10 = ( 2 / 10 * 100) % = 200 / 10 = 20 %
ii) 0.06 = 6 / 100 = ( 6 / 100 * 100) % = 600 / 100 % = 6%
iii) 0.008 = 8 / 1000 = ( 8 / 1000 * 100 ) % = 800 / 1000 % = 8 / 10 % = 4 / 5 % = 0.8 %
iv) 2.4 = 24/10 = ( 24 / 10 * 100 ) % = 2400 /10 % = 240 %
* Convert a Percentage into a Decimal
Rule : First convert the given percentage into a fraction and then convert this fraction into decimal form.
Express each of the following percentage as a decimal .
i) 25 % = 25 / 100 = 0.25
ii) 4 % = 4 / 100 = 0.04
iii) 3 1/5 % = 16/5 % = 16 / 500 = 4 / 125 = 0.032
Find the valve of :
i) 33% of ₹50 = 33/100 * 50 = 1650 / 100 = ₹16.50
ii) 6 2/3 % of 3 m = 20 / 3% of 3 m = 20 /300 of 300 cm = 6000 / 300 cm = 20 cm
iii) 0.6 % of 35 kg = 6/100 of 3500 g = 6 / 100 * 3500 g = 210 g
iv) 3 1/4 % of 5 lit = 13/4 % of 5000 ml = 13/ 400 * 5000 ml = 65000 / 400 ml = 162.5 ml
Express one quantity as a Percentage of other quantity.
x as a percentage of y = [(x/y) * 100]%
Exercise 1:
i) What percent of ₹ 9 is ₹ 5 ?
Ans : ₹ 9 = 900 paise and ₹ 5 = 500 paise
Required percentage = ((500 / 900 ) * 100 )%
= 500 / 9 %
= 55 (5/9) %
ii) What percent of 32m is 80 m ?
Ans : Required percentage = (80 / 32 *100) %
= 8000/ 32 %
= 250 %
iii) What percent of 50 kg is 65kg ?
Ans : Required percentage = ( 65/50 * 100 ) %
= 6500 / 50 %
= 650/5 %
= 130 %
iv) What percent of 5 litres is 400 ml ?
Ans : 5 litres = 5000 ml
Required percentage = (400/5000 * 100 ) %
= 40000 / 5000 %
= 8 %
Exercise 2:
i) If 8 % of a number is 24, find the number.
Ans : Let the number be x
8 % of x = 24
8/100 * x = 24
x = 24 * 100 / 8
x = 300
The number is 300
ii) If 7.25% of a number is 2.9 , find the number .
Ans : Let the number be x.
7.25 % of x = 2.9
7.25 / 100 * x = 2.9
x = 2.9 * 100 / 7.25
x = 290 / 7.25
x = 29000/ 725
x = 40
The number is 40
iii) If 6 2/3 % of a number is 1 . Find the number.
Ans : Let the number be x
6 2/3 % of a number x = 1
20 / 300 * x = 1
x = 1 * 300 / 20
x = 300 / 20
x = 15
The number is 15
Exercise :
i) Increase 75 by 24%
Ans : Required Number = ( 100 + 24 ) % of 75
= (124 / 100 ) * 75
= 124 *3/4
= 93
ii) Decrease 375 by 8%
Ans : Required Number = ( 100 - 8 ) % of 375
= 92 /100 * 375
= 92 * 3.75
= 345
iii) What number when increased by 15% becomes 276
Ans : Let the number be x
x + 15x/100 = 276
115x/100 = 276
115 x = 276 * 100
x = 27600 / 115
x = 240
The number is 240.
Word Problems Based on Percentage
Exercise :
Q 1 . 36% of the students in the school are girls. If the number of boys is 1440, find the total strength of the school.
Solution : Let the total strength of the school be x.
36% are girls , so % of boys = 100 - 36 = 64 %
so, 64% boys of total strength = 1440
64/100 * x = 1440
x = 1440 * 100/64
x = 2250
the total strength of the school = 2250
Q 2. Geeta saves 18% of her monthly salary. If she spends ₹ 10250 per month, what is her monthly salary?
Solution : Let her monthly salary be x.
She saves 18 % means she spend 100 - 18 = 82 %
82 % of her monthly salary = 10250
82 /100 * x = 10250
x = 10250 * 100 /82
x = 1025000/82
x = ₹ 12500
her monthly salary is ₹ 12500
Q 3 . In an examination, a student has to secure 40% marks to pass. Rahul gets 178 marks and fails by 32 marks. What are the maximum marks ?
Solution : Let the maximum marks be x.
Rahul gets 178 marks and he wants more 32 marks to pass.
means marks required to pass = 178 + 32 = 210
40 % marks of maximum marks = 210
40 /100 * x = 210
x = 210 * 100 /40
x = 21000/40
x = 525
the maximum marks = 525
Q 4 . 8% of students in a school remained absent on a day. If 1633 attended the school on that day, how many remained absent ?
Solution : Absent students = 8%
present student = 100 - 8 = 92 %
let the total student be x.
92 % of total student = 1633
92/100 * x = 1633
x = 1633 * 100 / 92
x = 163300 / 92
x = 1775
Total students = 1775
8% of 1775 = absent student
8/100 * 1775 = absent student
14200 / 100 = absent student
Number of absent student =142
Q 5 . On increasing the price of an article by 14 % , it becomes ₹ 1995. What was its original Price ?
Solution : Let the original price be x.
Increase in price = 14 %
Increased price = ₹ ( 1 + 14/100) x
1995 = 114x /100
x = 1995 * 100/114
x = ₹ 1750
The original price is ₹ 1750
Q. 6. On decreasing the price of an article by 6 % , it becomes ₹ 1551. What was its original Price ?
Solution : Let the original price be x.
decrease in price = 6 %
decreased price = ₹ ( 1 - 6/100) x
1551 = 94x /100
x = 1551 * 100/94
x = ₹ 1650
The original price is ₹ 1650
Q. 7. Reenu reduced her weight by 15 %. If now she weighs 52.7kg, what was her earlier weight ?
Solution : Let her earlier weight be x.
she reduced by 15 %
x - 15% of earlier weight = 52.7 kg
x - 15x/100 = 52.7
100x - 15x/100 = 52.7
85x /100 = 52.7
x = 52.7 * 100/85
x = 5270/85
x = 62 kg
Her earlier weight was 62 kg.
Q. 8. Two Candidates contested an election. One of them secured 58 % votes and won the election by a margin of 2560 votes. How many votes were polled in all ?
Solution : Let the total number of votes be x.
one candidate secured 58%, means
percentage of votes secured by other candidates = 42 %
so, ( 58 - 42) % of total number of votes = 2560
16% of x = 2560
16/100 * x = 2560
x = 2560 * 100 /16
x = 16000 votes
The total number of votes = 16000
Q 9 : In an examination , Preeti scored 60 out of 75 in science, 84 out of 100 in Mathematics, 36 out of 50 in Hindi and 30 out of 45 in English.
i) In which subject her performance is worst ?
ii) In which subject her performance is best?
iii) What is her aggregate percentage of marks ?
Solution :
Percentage in Science = (60/75 * 100) %
= 6000/75 = 80 %
Percentage in Mathematics = 84/100 * 100) %
= 8400/100 = 84 %
Percentage in Hindi = (36/50 * 100) %
= 3600/50 = 72 %
Percentage in English = (30/45 * 100) %
= 3000/45 = 66.6 %
iii) Her aggregate percentage of marks = ( 60+84+36+30/75+100+50+45) * 100 %
= 77.77 %
Q .10 . The price of an article is increased by 25 % . By how much percent must this new value be decreased to restored it to its former value ?
Solution : Let original price = ₹ 100
Increased price = ₹ 125
Decreased in price required = ₹ ( 125 -100) = ₹ 25
Required % = 25 /125 *100
= 2500/125
= 20 %
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