Selina Concise Solutions for Chapter 8 Percent and Percentage Class 7 ICSE Mathematics

Exercise 8(A)


1. Express each of the following as percent :
(i) 3/4 
(ii) 2/3
(iii) 0.025
(iv) 0.125
(v) 3/8
(vi) 0.25

Answer 


2. Express the following percentages as fractions and as decimal numbers : 
(ii) 2.50%
(iii) 0.02%
(iv) 175%
(v) 5 %
(vi) 25%
Answer 

3. What percent is :
(i) 16 hours of 2 days ?
(ii) 40 paisa of Rs. 2 ?
(iii) 25 cm of 4 metres
(iv) 600 gm of 5 kg ?
Answer 

4. Find the value of : 
(i) 5 % of Rs. 350 
(ii)10% of Rs. 400.40 
(iii) 1 % of Rs. 500

(v) 5/8 % of Rs. 600 
Answer 

5. In a class of 60 children, 30% are girls. How many boys are there  ?
Answer 
Total children = 60, 
Girls = 30% 
∴ Total girls = 30% of 60 = 60 × 30/100 = 18 
∴ No. of boys = 60 - 18 = 42 

6. In an election, two candidates A and B contested. A got 60 % of the votes. The total votes polled were 8000. How many votes did each get ? 
Answer 
Total number of votes polled = 8000
A got 60% of the votes
A got total votes = 60% of 8000 = 8000 × 60/100  = 4800
∴ B got total votes = 8000 – 4800 = 3200

7. A person saves 12% of his salary every month. If his salary is ₹2,500, find his expenditure.
Answer 
Total salary = ₹2500
Saving = 12% of the salary
∴ Total savings = 12% of ₹2500
= ₹2500 × 12/100 = ₹300
∴Total expenditure = ₹2500 – ₹300 = ₹2200

8. Seeta got 75% marks out of a total of 800. How many marks did she lose ?

Answer 

Total marks = 800
Marks Seeta got = 75% of total marks
∴ Total marks Seeta got = 75% of 800
= 800 × 75/100  = 600
∴ Marks Seeta lose = 800 – 600 = 200


9. A shop worth ₹25,000 was insured for 95% of its value. How much would the owner get in case of any mishappening ?

Answer 

Value of shop =₹25,000
Insured amount = 95% of total value
= 95% of ₹25,000
= ₹25,000 × 95/100
= ₹ 23,750


10. A class has 30 boys and 25 girls. What is the percentage of boys in the class ?

Answer 

No. of boys = 30
No. of girls = 25
Total number of children = 30 + 25 = 55
∴ Percentage of boys in the class
= 30/55  × 100
= 600/11 %


11. Express :
(i) as a percent
(ii) 0.0075 as percent
(iii) 3 : 20 as percent
(iv) 60 cm as percent of 1 m 25 cm
(v) 9 hours as a percent of 4 days.

Answer 


12. (i) Find 2% of 2 hours 30 min.
(ii) What percent of 12 kg is 725 gm?

Answer 

(i) 2 % of 2 hours 30 min
∵ 1 hour = 60 minutes
∴ 2 hours  30 min. = 2 × 60 min. + 30 min. 
= 120 + 30 = 150 min
= 150 ×(2/100) = 30/10
= 3 minutes
(ii) 12 kg is 725 gm 
1 kg = 1000 gm 
∴ 12 kg = 12 × 1000 = 12000 gm 
725/12000 × 100 = 725/120


Exercise 8 (B)


1. Deepak bought a basket of mangoes containing 250 mangoes 12% of these were found to be rotten. Of the remaining, 10% got crushed. How many mangoes were in good condition ?
Answer
Total mangoes = 250 
Rotten mangoes = 12 % of 250 
= 250 × 12/100 = 30 
Remaining mangoes = 250 - 30 =220
Mangoes which were crushed = 10% of 220 
= 220 × 10/100 = 22 
∴ Balance = 220 - 22 = 198 
Hence 198 mangoes were in good condition.


2. In a Maths Quiz of 60 questions, Chandra got 90% correct answers and Ram got 80% correct answers. How many correct answers did each give? What percent is Ram’s correct answers to Chandra’s correct answers ?
Answer 
No. of total questions = 60 
Chandra got correct answers of the questions
= 90% of 60 
= (60×90)/100 = 54 
Ram got correct answers of the questions 
= 80% of 60 
= 60 × (80/100) = 48 
∴ Percentage of Ram's correct answer of 

3. In an examination, the maximum marks are 900. A student gets 33% of the maximum marks and fails by 45 marks. What is the passing mark ? Also, find the pass percentage.
Answer 
Maximum marks = 900 
A student got 33% of 900 marks
= 900 × (33/100) = 297 
No. of marks by which he failed = 45 
∴ Pass marks = 297 +45 = 342
Percentage of pass marks = (342 ×100)/900
= 38 % 

4. In a train, 15% people travel in first class, 35% travel in second class. The balance travel in the A.C. class ? Calculate the percentage of A.C. class travellers ?
Answer 
Let no. of  people = 100 
No. of people in first class = 15 
and no. of people travel in second class = 35 
∴ Balance = 100 -(15 + 35) = 100 - 50 = 50 
∴ Percent of people travel in AC class = 50 % 

5. A boy eats 25% of the cake and gives away 35% of it to his friends. What percent of the cake is still left with him ?
Answer 
Let total cake = 100 
Cake which was eaten by the boy = 25 
Cake which was given to his friends = 35 
∴ Balance cake = 100 -(25 + 35)
= 100 - 60 = 40 
Hence he has 40 % of the cake with him.  

6. What is the percentage of vowels in the English alphabet ?
Answer 
There are 5 vowels in 26 English alphabets 
∴ Percentage of vowels = (5×100)/26

7.
(ii) 0.2 % of a number is  5. Find the number . 
Answer 


8. The money spent on the repairs of a house was 1% of its value. If the repair, costs Rs. 5,000, find the cost of the house.
Answer 
Let cost of house = x 
Then cost of repairs = 1% of x 
∴ 1 % of x = 5000

x = 5, 00, 000
Hence cost of house = Rs. 5,00,000

9. In a school out of 300 students, 70% are girls and  30% are boys. If 30 girls leave and no new boy is admitted, what is the new percentage of girls in the school ? 
Answer 
Total number of children in a school = 300 
No. of boys = 30% of 300 
= (30/100) × 300 = 90 
and no. of girls = 70 % of 300 
= (70/100)×300 =210
Now no. of girls left = 30 
∴ No. of girls after leaving 30 girls = 210 - 30 = 180 
and No. of children in the school 
= 180 + 90  =270 
∴ % of girls now = (180/270) ×100 = 200/3%
= 

10. Kumar bought a transistor for Rs. 960. He paidcash money. The rest he agreed to pay in 12 equal monthly instalments. How much will he pay each month ? 
Answer 
Price of transistor = Rs. 960
Amount paid in cash =of Rs. 960

Balance amount = Rs. 960 - Rs. 120
= Rs. 840
No. of instalments = 12
∴ Amount of each instalment
= Rs. 840 ÷ 12 = Rs. 70

11. An ore contains 20% zinc. How many kg of ore will be required to get 45 kg of zinc ?
Answer 
In an ore, zinc = 20% 
Let quantity of ore = x 
∴ 20% of x = 45 kg 
⇒ (20/100) × x = 45 
⇒ x/5 = 45 
⇒ x = 45× 5= 225 
∴ quantity of ore = 225 kg 

Exercise 8 (C)


1. The salary of a man is increased from Rs. 600 per month to Rs. 850 per month. Express the increase in salary as percent.
Answer 
Original salary of a man = Rs. 600 
Increased salary = Rs. 850 
∴ Amount of increase = Rs. 850 - 600 = Rs. 250 
Percentage increase = (250 ×100)/600 = 125/3

2. Increase : 
(i) 60 by 5%
(ii) 20 by 15%
(iii) 48 by
(iv) 80 by 140%
(v) 1000 by 3.5%
Answer 
(i) Rate of increase = 5 % 
∴ Total increase = 5 % of 60 = (5/100)× 60  = 3 
∴ Increased number = 60+3 = 63 

3. Decrease :
(i)80 by 20%
(ii) 300 by 10%
(iii) 50 by 12.5%
Answer 
(i) Decrease on 80 by 20% = 80 × (20/100) = 16 
∴ Decreased number = 80 - 16 = 64 
(ii) Decrease on 300 by 10% = 300 × (10/100) = 30 
∴ Decrease number = 300- 30 = 270 
(iii) Decrease on 50 by 12.5% = 50 ×(12.5/100)
= 50 × (125/1000) = 25/4 = 6.25 %
∴ Decrease number = 50 -6.25 
 = 43.75 

4. What number :
(i) When increased by 10% becomes 88 ?
(ii) When increased by 15% becomes 230 ?
(iii) When decreased by 15% becomes 170 ?
(iv) When decreased by 40% becomes 480 ?
(v) When increased by 100% becomes 100 ?
(vi) When decreased by 50% becomes 50 ?
Answer 
(i) Let the number  be = 100 
Increase = 10% = 10 
∴ Increase number = 100 + 10 = 110 
If increased number is 110, then original number = 100
and if increased number is 88, then original number = (100/110) × 88 = 80 

(ii) Let the number be = 100 
Increase = 15% = 15 
∴ Increased number = 100 +15 = 115 
If increased number is 115, then original number = 100 
and if increased number is 230, then original number = (100×230)/115 = 200 

(iii) Let the number be = 100 
Decrease = 15 % = 15 
∴ Decreased number = 100 -15 =  85 
If decreased number is 85, then original number = 100 
and if decreased number is 170, then original number = (100/85) × 170 = 200 

(iv) Let the number be  = 100 
Decrease = 40%  = 40 
∴ Decreased number = 100 -40 = 60 
If decreased number is 60, then original number = 100 
and if decreased number is 480 , then original number = (100× 480)/60 = 800 

(v) Let the number be = 100 
Increase = 100%  = 100 
∴ Increased number = 100 + 100 = 200 
If increased number is 200, then original number = 100 
and if increased number is 100, then original number = (100×100)/200 = 50

(vi) Let the number  be = 100 
Decrease = 50 % = 50 
∴ Decreased number = 100 -50 = 50 
If decreased number  is 50, then original number = 100 
and if decreased number  is 50, then original number = (100×50)/50 = 100

5. The price of a car is lowered by 20% to Rs. 40,000. What was the original price ? Also, find the reduction in price.
Answer 
Let original price of the car = Rs. 100
Reduction = 20%’ = Rs. 20
∴ Reduced price = Rs. 100 – 20 = Rs. 80
If reduced price is Rs. 80, then original price = Rs. 100
and if reduced price is Rs. 40,000 then original price = Rs. (100×40,000)/80 = Rs. 50, 000
and reduction = Rs. 50,000 - Rs. 40000
= Rs. 10,000

6. If the price of an article is increased by 25%, The increase is Rs. 10. Find the new price.
Answer 
Let the price of an article = Rs. 100
Increase = 25%
∴Increase = Rs. 25
If an increased price = Rs. 100 + 25 = Rs. 125
If increase is Rs. 25 then new price = Rs. 125
and if increase is Rs. 10, then new price = Rs. (125×10)/25
= Rs. 50

7. If the price of an article is reduced by 10%, the reduction is Rs. 40. What is the old price ?
Answer 
Let the original (old) price = Rs. 100
Reduction = 10% = Rs. 10
∴If reduction is Rs. 10, then old price = Rs. 100
and if reduction is Rs. 40, then old price = Rs. (100×40)/10 = Rs. 400

8. The price of a chair is reduced by 25%. What is the ratio of:
(i) Change in price to the old price.
(ii) Old price to the new price.
Answer 
Let old (original) price of a chair = Rs. 100
Reduction = 25% = Rs. 25
∴ Reduced price = Rs. 100 – Rs. 25 = Rs. 75
(i) Ratio between change in price and old price = 25 : 100
= 1:4 (Dividing by 25)
(ii) Ratio between old price and new price = 100 : 75
= 4:3 (Dividing by 25)

9. If x is 20% less than y, find: 
(i) x/y  
(ii) (y-x)/y 
(iii) x/(y-x)
Answer 
Let y = 100 
then reduction = 20% = 20 
then x  = 100 - 20 = 80

10.  If x is 30% more than y; find : 
(i) x/y 
(ii) (y+x)/x 
(iii) y/(y-x)
Answer 
Let y = a

11.  The weight of a machine is 40 kg. By mistake it was weighed as 40.8 kg. Find the error percent. 
Answer 
Actual weight of machine = 40 kg 
Errored weight = 40.8 kg 
∴ Error in weight = 40.8 - 40 = 0.8 kg
Error % = (0.8 × 100)/40 = (8× 100)/(10×40) = 2%

12. From a cask, containing 450 litres of petrol, 8% of the petrol was lost by leakage and evaporation. How many litres of petrol was left in the cask ?
Answer 
Original petrol in the cask = 450 litres
Leakage and evaporation = 8 % 
∴ Lost petrol = 8% of 450 litres = (8× 450)/100 = 36 litres 

13. An alloy consists of 13 parts of copper, 7 parts of zinc and 5 parts of nickel. What is the percentage of each metal in the alloy? 
Answer 
Copper = 13 parts, Zinc = 7 parts , Nickel = 5 parts 
Total alloy = 13 + 7 + 5 = 25 parts 
Now, percentage of copper = (13/25) × 100 = 52 %
Percentage of zinc = (7/25) × 100 = 28%
and percentage of nickel = (5/25) × 100 = 20% 

14. In an examination, first division marks are 60%. A student secures 538 marks and misses the first division by 2 marks. Find the total marks of the examination.
Answer 
Percentage for first division = 60% 
A student secures 538 marks but misses the first division by 2 marks. 
∴ Marks for first division = 538 + 2 = 540 
∴ 60% of total marks = 540 
⇒ (60/100)× total marks = 540 
⇒ total marks = (540× 100)/60 = 900 

15. Out of 1200 pupils in a school, 900 are boys and the rest are girls. If 20% of the boys and 30% of the girls wear spectacles, find :
(i) how many pupils in all, wear spectacles ?
(ii) what percent of the total number of pupils wear spectacles ?
Answer 
Total number of pupils = 1200 
No. of boys = 900 
and no. of girls = 1200 - 900 = 300 
No. of boys who wear spectacles 
= 20% of 900 = (20/100)× 900  = 180 
No. of girls who wear spectacles 
= 30% of 300 = (30/100)× 300= 90 
(i) ∴ Total number of pupils who wear spectacles = 180 +90 = 270 
(ii) Percentage of pupils who wear spectacles 
= (270 × 100)/1200 = 270/12 = 22.5%

16. Out of 25 identical bulbs, 17 are red, 3 are black and the remaining are yellow. Find the difference between the numbers of red and yellow bulbs and express this difference as percent. 
Answer 
Total number of bulbs  = 25 
Number of red bulbs = 17 
Number  of  black bulbs = 3 
= 17 +3 = 20 
∴ Number  of yellow bulbs  = 25 - 20 = 5 bulbs 
Difference between the number of red and yellow bulbs 
= No. of red bulbs - No. of yellow bulbs 
= 17 - 5 = 12 
∴ Percentage difference 
= (Difference in red and yellow bulbs)/ Total number of bulbs 
=  (12/25)× 100 = 48%

17. A number first increases by 20% and then decreases by 20%. Find the percentage increase or decrease on the whole. 
Answer 
Let the number  be 100 
In 1st condition, 
Increase = 20% of 100 
= (20/100) × 100 = 20 
∴ Number  after this increase = 100 +20 = 120 
In 2nd condition, 
Decrease = 20% of 120 
= (20/100)× 120 = 24 
∴ Number  after this decrease = 120 - 24 = 96 
⇒ Total decrease on the whole = 24 -20 = 4 
and the percentage decrease on the whole = (4/100)× 100 = 4%

18.  A number is first decreased by 40% and then again decreased by 60%. Find the percentage increase or decrease on the whole.
Answer 
Let the number be 100 
In first condition : 
Decrease = 40% of 100 
= (40/100)× 100 = 40 
∴ Number after this decrease 
 = 100 -40 = 60 
In Second condition : 
Decrease = 60 % of 40 
= (60/100)× 40 = 24 
∴ Number after the 2nd decrease 
= 40 - 24 = 16 
⇒ Total decrease on the whole = 40 + 24 = 64 
∴ Percentage decrease on the whole = (64/100)× 100 = 64%

19. If 150% of a number is 750, find 60% of this number.
Answer 
Let the required number  be x 
Now, 150% of x = 750 
⇒ (150/100) × x = 750
⇒ x = (750× 100)/150 = 500 
Hence, the required number = 500 
Now, 60% of 500 = 500 × (60/100) = 300
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