# 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%

(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 :**

**Answer**

**5. In a class of 60 children, 30% are girls. How many boys are there ?**

**Answer**

Girls = 30%

∴ Total girls = 30% of 60 = 60 × 30/100 = 18

**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**

A got 60% of the votes

**7. A person saves 12% of his salary every month. If his salary is ₹2,500, find his**

**expenditure.**

**Answer**

**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**

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**

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**

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**

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**

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**

∴ Percentage of vowels = (5×100)/26

**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**

Then cost of repairs = 1% of x

∴ 1 % of x = 5000

**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**

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**

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**

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**

Increased salary = Rs. 850

∴ Amount of increase = Rs. 850 - 600 = Rs. 250

Percentage increase = (250 ×100)/600 = 125/3

**2. Increase :**

**Answer**

∴ 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**

∴ 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**

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

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

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

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

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

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**

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**

**7. If the price of an article is reduced by 10%, the reduction is Rs. 40. What is the old price ?**

**Answer**

**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**

**9. If x is 20% less than y, find:**

(i) x/y

(ii) (y-x)/y

(iii) x/(y-x)

(i) x/y

(ii) (y-x)/y

(iii) x/(y-x)

**Answer**

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)

(ii) (y+x)/x

(iii) y/(y-x)

**Answer**

**11. The weight of a machine is 40 kg. By mistake it was weighed as 40.8 kg. Find the error percent.**

**Answer**

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**

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**

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**

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**

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**

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**

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**

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**

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