Percentage-Profit and Loss - Testlabz©EDULABZ INTERNA TIONAL Math Class VIII 5 Question Bank Amount...

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Math Class VIII 1 Question Bank

1. 36% of the students in a school are girls. If the number of boys is

1440, find the total strength of the school.

Ans. Let total number of students in the school be x

Total number of boys in school = 1440

Number of girls in school = 36% of x = 36

100x

∴ Number of boys in school = 36

100

xx − =

641440

100

x=

Thus, 1440 100

225064

x×

= =

Hence, number of total students is 2250

2. Reeta saves 18% of her monthly salary. If she spends Rs 10250 per

month, what is her monthly salary?

Ans. Monthly saving of Reeta = 18%

and monthly expenditure of Reeta = Rs 10250

Let monthly income of Reeta be Rs x

then, saving of Reeta = 18% of x = 18

100x

and expenditure of Reeta = 18 82

100 100x x x− =

Thus 82

100x = 10250 ⇒

10250 100

82x

×=

⇒ x = 12500

Hence, monthly income of Reeta is Rs 12500.

3. In an examination, a student has to secure 40% marks to pass. Rohit

gets 178 marks and fails by 32 marks. What is the maximum marks?

Ans. Rohit gets marks = 178

8PERCENTAGE - PROFIT

AND LOSS

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Marks by which Rohit fails = 32

Thus pass marks for Rohit = 178 + 32 = 210

But pass marks is 40%

∴ 40% of total marks = 210

Total marks = 210 100

52540

×=

Hence, 525 is the maximum marks.

4. In a straight contest, the loser polled 42% votes and lost by 14400

votes. Find the total number of votes polled. If the total number of

eligible voters was 1 lac, find what percentage of voters did not vote.

Ans. Since the losing candidate secured 42% of the votes polled

Thus winning candidate secures

= (100 – 42)% of the votes polled = 58% of the votes polled

Difference of votes = 58% – 42% = 16% of the votes polled

Thus 16% of the votes polled = 14400

⇒16

100 of the votes polled = 14400

⇒ votes polled = 100

1440016

× = 900 × 100 = 90000

Total number of eligible voters = 100000 (Given)

Number of voter who did not vote = eligible voters – votes polled

= 100000 – 90000 = 10000

Thus, percentage of the number of voters who did not vote

= 10000

100 %100000

×

=

10000% 10%

1000=

Hence, 10% of voters did not vote.

5. Out of 8000 candidates, 60% were boys. If 80% of the boys and

90% of the girls passed the exam, find the number of candidates

who failed.

Ans. Total number of candidates = 8000

Number of boys candidates = 60% of 8000

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= 60

8000100

× = 60 × 80 =4800

Number of girls candidates = 8000 – 4800 = 3200

Number of passed boys = 80% of number of boys

= 80

4800100

× = 80 × 48 = 3840

Number of passed girls = 90% of number of girls

= 90

3200100

× = 90 × 32 = 2880

Thus number of passed candidates = 3840 + 2880 = 6720

and number of failed candidates = 8000 – 6720 = 1280

Hence, 1280 candidates are failed.

6. Out of 120 employees in a company, 80% are males. Eighty male

employees and three-fourth of the female employees are married. In

aggregate, what percent of company’s employees are married?

Ans. Total number of employees in the company = 120

Number of males employees in the company = 80% of 120

= 80

120 96100

× =

Number of female employees in the company = 120 – 96 = 24

Number of married employees in the company

= 3

80 of 244

+

= 80 + 18 = 98

Percentage of married employees in the company

= 98 98

100% 10%120 12

× = ×

= 98 49

5% 5%6 3

× = × = 245 2

81 %3 3

=

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Hence, 2

81 %3

of company’s employees are married.

7.(i) A number 3.625 is wrongly read as 3.265; find the percentage error.

(ii) A number 5.78 × 103 is wrongly written as 5.87 × 103 ; find the

percentage error.

Ans. (i) Correct number = 3.625

Number wrongly read = 3.265

Then error = (3.625 – 3.265) = 0.360

Thus, percentage error = 0.360

100%3.625

×

= 360 36000

100% % 9.93%3625 3625

× = =

Hence, percentage error is 9.93%.

(ii) Correct number = 5.78 × 103

Number wrongly written as = 5.87 × 103

Thus, error = 5.87 × 103 – 5.78 × 103 = 0.09 × 103

Thus percentage error =

3

3

0.09 10100%

5.78 10

××

× =

0.09100%

5.78×

9

100%578

= × 900

% 1.56%578

= =

Hence, percentage error is 1.56%.

8. Bhola Ram gave 35% of his money to his elder son and 40% of the

remainder to the younger son. Now, he is left with Rs 11700. How

much money had he?

Ans. Let Bhola Ram had Rs x.

Amount given to elder son = 35% of x = 35

100

x

Remaining amount = Rs 35 65

100 100

x xx

− =

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Amount given to his younger son = 65 40 26

100 100 100

xx× =

Amount left with him = Rs 65 26 39

100 100 100

xx x

− =

Thus, 39

11700100

x = ⇒ 11700 100

39x

×=

⇒ x = 30000

Hence, total amount Bhola Ram had = Rs 30000.

9. 5% of the population of a town were killed in an earthquake and 8%

of the remainder left the town. If the population of the town now is

43700, what was its population at the beginning?

Ans. Let population of the town at the beginning be x%

People killed in an earthquake = 5% of the population

Thus, total people killed = 5 5

100 100

xx × =

Then remaining population of the town = 5 95

100 100

x xx − =

Those people who left the town = 95 8 76

100 100 1000

xx× =

Hence, remaining population of the town = 95 76

100 1000

xx−

= 950 – 76 874

1000 1000

x xx=

∴ 87443700

1000x = ⇒

43700 100050000

874x

×= =

Hence, population of the town at the beginning was 50000.

10. A and B are two towers. The height of tower A is 20% less than that

of B. How much per cent is B’s height more than that of A?

Ans. Let height of tower B = 100 m

Since, height of tower A is 20% less than B

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∴ Height of tower A = 20

100 100100

− × =

100 – 20m = 80m

Thus, height of B which is more than A’s = (100 – 80)m = 20m

Percent of B’s height more than that of A = 20 100

25%80

×=

Hence, B’s height is 25% more than A’s height.

11. In an examination, 30% of the candidates failed in English, 35%

failed in GK and 27% failed in both the subjects. If 310 candidates

passed in both, how many candidates appeared in the examination?

Ans. Let total number of candidates who appeared in examination

= 100

Failed candidates in English = 30% of 100 = 30

Failed candidates in GK = 35% of 100 = 35

Failed candidates in both = 27% of 100 = 27

Thus, total failed candidates = 30 + 35 – 27 = 65 – 27 = 38%

∴ Total passed candidates = (100 – 38) = 62.

Hence total candidates = 100

310 50062

× =

Hence, 500 candidates appeared in the examination..

12. In a combined test in History and Civics; 36% candidates failed in

History; 28% failed in Civics and 12% in both; find :

(i) the percentage of passed condidates

(ii) the total number of candidates appeared, if 208 candidates have

failed.

Ans. Candidates failed only in History = 36% – 12% = 24%

Candidates failed only in Civics = 28% – 12% = 16%

Candidates failed in both subjects = 12%

Total failed candidates = 24% + 16% + 12% = 52%

(i) Thus percentage of passed candidates = 100% – 52% = 48%

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(ii) If failed candidates are 52,

then total appeared candidates = 100

If failed candidate is 1, then total appeared candidates = 100

52If failed candidates are 208,

then total appeared candidates = 100

20852

×

= 100 × 4 = 400

13. Nandani purchased some parrots. 20% flew away and 5% died. Of

the remaining, 45% were sold. Now 33 parrots remain. How many

parrots had Nandani purchased?

Ans. Let Nandani purchased x parrots.

Then number of parrots flew away = 20% of x

= 20

100x× =

1

5 5

xx× =

Number of died parrots = 5% of x = 5

100 20× =

xx

Number of remaining parrots = –5 20

x xx

+

=

4

20

x xx

+ −

= 5

20 4

x xx x− = − =

4 3

4 4

x x x−=

Number of parrots sold = 45% of 3

4

x =

45 3

100 4

x×

= 9 3 27

20 4 80

x x× =

Number of those parrots which are not sold

= 3 27

4 80

x x− =

60 27 33

80 80

x x x−=

As per condition,

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33

3380

x= ⇒ 33x = 33 × 80

⇒ 33 80

33x

×= ⇒ x = 80

Hence, Nandani purchased 80 parrots.

14. A lunch interval of half an hour is 5% of total office hours. Calculate

(i) the total office hours (ii) the working hours

Ans. (i) 5% of total office hours = 1

2 hour

⇒5

100 of total office hours =

1

2hour

⇒ total office hours = 100

5 2× hours = 10 hours.

(ii) Working hours = 10 hours – 1

2 hours

= 1

102

−

hours =

19

2 hours =

19

2 hours.

15. Price of bananas has changed from 5 for a rupee to 4 for a rupee.

Find the percentage increase in the price.

Ans. Original price of 5 bananas = Rs 1

∴ Original price of 1 banana = Rs 1

5Changed price of 4 bananas = Rs 1

∴ Changed price of 1 banana = Rs 1

4

Increased price = Rs 1 1

4 5

−

= Rs

5 4

20

−

= Rs 1

20

Hence, percentage increased price =

1

20 100%1

5

×

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= 1 5

100%20 1

× ×

1100% 25%

4= × =

16. Two numbers are respectively 25% and 35% less than a third number.

What percent is the second number of the first?

Ans. Let the third number be x

Then, first number = 25

1100

x

−

= 75 3

100 4x x=

And, second number = 35

1100

x

−

= 65 13

100 20x x=

Thus, required percentage =

13

20 100%3

4

x

x

× = 13 4

100%20 3

xx

× ×

= 13

100%5 3

××

= 13 260

20% %3 3

× =

= 2

86 %3

17. 75% of the students in a class VIII passed an exam. If 2 more students

had passed the exam, 80% would have been successful. How many

students were there in the class VIII?

Ans. Let the total number of students in the class VIII be x,

Number of passed students in the calss VIII = 75% of x

= 75 75

100 100

xx× =

As per condition,

75

2 80%100

x+ = of x

⇒ 75 80

2100 100

xx+ = × ⇒

75 802

100 100

x x+ =

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⇒ 80 75

2100 100

x x= − ⇒ 5

2100

x=

⇒ 220

x= ⇒ 2

20

x=

⇒ 2 20x = × ⇒ 40x =

Hence, the total number of students in class VIII were 40.

18. The monthly salary of a school teacher in 2005 was Rs. 12000. It

increased by 10% in 2006 and again by 10% in 2007. What is his

salary in 2007?

Ans. Monthly salary of the school teacher in 2005 = Rs 12000

Monthly salary of the school teacher in 2006 = Rs 10

1 12000100

+ ×

= Rs 110

1200100

×

= Rs

1112000

10×

= Rs 11 × 1200 = Rs 13200

Monthly salary of the school teacher in 2007

= 10

1100

+

Rs 13200

= Rs 110

13200100

×

= Rs

1113200

10×

= Rs 11 × 1320 = Rs 14520

Hence, monthly salary of the school teacher in 2007 = Rs 14520

19. Dolly’s height increased by 20% last year and by 15% this year. What

is the total percent increase in 2 years?

Ans. Let the original height of Dolly be x

Increased height in last year = 20

1100

x

+ ×

= 120 120

100 100

xx× =

Increased height in this year = 15 120

1100 100

x + ×

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= 115 120 23 6

100 100 20 5

x x× = × =

138

100

x

Total increases in 2 years = 138

100

xx− =

138 100 38

100 100

x x x−=

Total percentage increases in 2 years =

38

100 100%

x

x×

= 38

100% 38%100

x

x× =

×

Hence, 38% increase in 2 years.

20. Price of a commodity decreased by 10% last year and increased by

20% this year. Find the percentage change in two years.

Ans. Let the price of commodity be Rs x

When the price of commodity is decreased by 10% in last year

Then price of commodity in last year = 10

1 Rs100

x

− ×

= Rs 90

10x = Rs

9

10

x

When the price of commodity increased by 20% in this year

Then price of commodity in this year = 20

1100

+ ×

Rs

9

10

x

= Rs 1 9

15 10

x + ×

= Rs 6 9

5 10

x× = Rs

27

25x

Increased of price of commodity in these 2 years

= 27 27 – 25

–25 25

x x xx = =

2

25

x

Hence, percentage increased in these 2 years

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=

2

225 100% 100%25

x

x

x x× = ×

×

= 2 × 4% = 8%

21. The length and the breadth of a rectangle are 10 cm and 8 cm. If its

length increases by 15% and breadth by 20%, find the percentage

increase in its area.

Ans. Length of rectangle increases by 15% and the breadth increases by20% (given)

New length of rectangle = 15

1100

+

of 10 cm

= 115 115

10cm cm100 10

× = = 11.5 cm

New breadth of rectangle = 20

1100

+

of 8 cm

= 120

8cm100

× = 6

8cm5

×

= 48

cm 9.6cm5

=

Thus, new area of rectangle = (11.5 × 9.6) cm2 = 110.4 cm2

Original area of rectangle = (10 × 8) cm2 = 80 cm2

Thus, increase in area = (110.4 – 80) cm2 = 30.4 cm2

∴ Percentage increase in area = 30.4 30.4

100 % 5 %80 4

× = ×

= (7.6 × 5)% = 38%

Hence, the area of the rectangle is increased by 38%.

22. Two numbers are respectively 20 percent and 50 percent more than athird number. What percent is the second of the first?

Ans. Let the third number be x.

∴ First number = 20

100x x+ =

100 20 120

100 100

x x x+=

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Second number = 50

100x x+ =

100 50 150

100 100

x x x+=

Thus, required percent =

150

100120

100

×

x

x 100% =

150 100100

100 120

x

x× × %

150 100

120

×= % =

1500% 125%

12=

23. Two numbers are respectively 30 percent and 40 percent less than a

third number. What percent is the second of the first?

Ans. Let the third number be x

∴ First number = 30

100

xx − =

100 30 70 7

100 100 10

x x x x−= =

and second number = 40

100

xx − =

100 40 60 6

100 100 10

x x x x−= =

Thus, required percentage =

6

10 1007

10

x

x×

= 6 10 600 5

100 85 %10 7 7 7

x

x× × = =

Hence, 5

857

percentage of the first is the second.

24. During 2006, the production of a publication factory decreased by

25%. But, during 2007, it (production) increased by 40% of what it

was at the beginning of 2007. Calculate the resulting change (increase

or decrease) in production during these two years.

Ans. Let at the begining of 2006, production = 100

decrease in production = 25%

Thus, new production = 100 – 25 = 75

In 2007, it is increased by 40%

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∴ Increase in production = 75 40

30100

×=

∴ New production = 75 + 30 = 105

∴ Resulting change in two years (increase) = 105 – 100 = 5Hence, precentage change in increase in production

= 5

100% 5%100

× =

25. Motilal bought a certain number of oranges at Rs 60 per score and

sold them at 20% profit. Find the selling price of each orange.

Ans. Cost price of 20 oranges = Rs 60 (∵ 1 score = 20)

∴ Cost price of 1 orange = 60

20 = Rs 3

Profit = 20%

∴ Selling price of 1 orange = 3 120 360

100 100

×= = Rs 3.60

26. Nakvi sells two articles for Rs 4,500 each, making 25% profit on

one and 25% loss on the other. Find:

(i) CP of each article.

(ii) total CP of both the articles.

(iii) total SP of both the articles.

(iv) profit % or loss % on the whole.

Ans. (i) Selling price of two articles = Rs 4500 each.

Cost price of one = 100 4500 100 4500

100 25 125

× ×=

+

= 4

4500 4 9005

× = × = Rs 3600

Cost price of other = 100 4500 100 4500

100 25 75

× ×=

−

= 4

4500 4 15003

× = × = Rs 6000

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(ii) Total cost price of both the articles = Rs 3600 + Rs 6000

= Rs 9600

(iii) Total selling price of both the articles = Rs 2(4500) = Rs 9000

(iv) Loss = Rs (9600 – 9000) = Rs 600

Loss % = 600 100 25

100% % % 6.25%9600 16 4

× = = =

27. A wine bottle was sold at a loss 8%. Had it been sold for Rs 56

more, there would have been a gain of 8%. What is the cost price of

the wine bottle?

Ans. Let cost price of the wine bottle be Rs x

Loss = 8% of x = 8 2

100 25

xx× =

∴ Selling price of the wine bottle = 2

25

xx − =

25 2 23

25 25

x x x−=

Now, gain = 8% of x = 8 2

100 25

xx× =

Thus, selling price of the wine bottle = 2

25

xx +

= 25 2 27

25 25

x x x+=

∴27 23

– 5625 25

x x= ⇒

27 2356

25

x x−= ⇒

456,

25

x=

⇒ 56 25

,4

x×

= ⇒ 350.x =

Hence, cost price of the wine bottle = Rs 350.

28. The selling price of 18 mangoes is equal to the cost price of 21mangoes. Find the gain or loss per cent.

Ans. Let cost price of each mangoes = Re 1

Cost price of 18 mangoes = Rs 18

Selling price of 18 mangoes = Cost price of 21 mangoes = Rs 21

Gain = Rs (21 – 18) = Rs 3

Hence, gain % = 3 50 2

100% % 16 %18 3 3

× = =

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29. The cost price of 12 fans is equal to the selling price of 16 fans. Findthe gain or loss per cent.

Ans. Let selling price of one fan = Rs 100

∴ Selling price of 16 fans = Rs 100 × 16 = Rs 1600

and cost price of 12 fans = Rs 1600

∴ Cost price of one fan = 1600

12 = Rs

400

3Loss = cost price – selling price

= Rs 400 100 400 300

3 1 3

− − =

= Rs

100

3

Loss percent =

100100

Loss 100 3% %400cost price

3

××

=

= 100 100 3

% 25%3 400

× ×=

×

30. A man buys two bats, one for Rs. 340 and the other for Rs 260. He

sells the first bat at a gain of 15% and the second one at a loss of

15%. Find the gain or loss per cent in the whole transaction.

Ans. Cost price of first bat = Rs 340

Gain = 15% of Rs 340 = Rs 15

340100

× = Rs 51

Selling price of first bat = Rs (340 + 51) = Rs 391

Now, cost price of second bat = Rs 260

Loss = 15% of Rs 260 = Rs 15

260100

× = Rs 39

Selling price of second bat = Rs (260 – 39) = Rs 221

∴ Total selling price of two bats = Rs (391 + 221) = Rs 612

Gain = Rs (612 – 600) = Rs 12

Hence, gain% = 12

100% 2%600

× =

Hence, his gain in whole transaction is 2%.

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31. Nandlal bought 20 dozen note-books at Rs 48 per dozen. He sold 8

dozens of them at 10% gain and the remaining 12 dozens at 20%

gain. What is his gain percent in the whole ransaction?

Ans. Cost price of 1 dozen note-books = Rs 48

Cost price of 20 dozen note-books = Rs 48 × 20 = Rs 960

Cost price of 8 dozen note-books = Rs 48 × 8 = Rs 384

Gain = 10% of Rs 384 = Rs 10

384100

× = Rs38.40

Selling price of 8 dozen note-books = Rs (384 + 38.40) = Rs 422.40

Now, cost price of 12 dozen note-books = Rs 48 × 12 = Rs 576

Gain % = 20% of Rs 576 = Rs 20

576100

× = Rs 115.20

Thus, selling price of 12 dozen note-books

= Rs (576 + 115.20) = Rs 691.20

Selling price of 20 dozen note-books

= Rs (422.40 + 691.20) = Rs 1113.60

∴ Whole gain = Rs (1113.60 – 960) = Rs 153.60

Gain% = 153.60

100% 16%960

× =

Hence, his gain percent in whole transaction is 16%.

32. A shopkeeper buys a certain number of pens. If the selling price of 5

pens is equal to the cost price of 7 pens, find his profit or loss

percentage.

Ans. Let the cost price of 7 pens be Rs x.

Cost price of 1 pen = Rs 7

x

As per condition,

Selling price of 5 Pens = Rs x

Selling price of 1 Pen = Rs 5

x

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Profit = selling priec – cost price = Rs 5

x – Rs

7

x

= Rs 7 5

35

−

x x = Rs

2

35

x

Profit % = Profit

100%cost price

× =

2

35 100%

7

x

x×

= 2 7

100%35

x

x× × =

2100% 2 20% 40%

5× = × =

Hence, profit percentage is 40%.

33. Coffee costing Rs 100 per kg was mixed with chicory costing Rs. 50

per kg in the ratio 5 : 2 for a certain blend. If the mixture was sold at

Rs. 90 per kg. Find the gain or loss per cent.

Ans. Cost price of 1 kg of coffee = Rs 100

Cost price of 5 kg of coffee = Rs 5 × 100 = Rs 500

Cost price of 1 kg of chicory = Rs 50

Cost price of 2 kg of chicory = Rs 2 × 50 = Rs 100

∴ Cost price of (5 + 2) kg of mixture

= Rs (500 + 100) = Rs 600

Now, selling price of 1 kg of mixture = Rs 90

Selling price of 7 kg of mixture = Rs 7 × 90 = Rs 630

Gain = Rs (630 – 600) = Rs 30

Hence, gain percent = 30

100% 5%600

× =

34. A sells a bicycle to B at a profit of 20% and B sells it to C at a profit

of 5%. If C pays Rs 1890, what did A pay for it?

Ans. C’s cost price for the cycle = Rs 1890

or B’s selling price = Rs 1890

gain = 5%

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∴ B’s cost price = cost price 100 1890 100

Rs100 gain% 100 5

× ×=

+ +

= Rs 1890 100

105

× = Rs 1800

or A’s selling price = Rs 1800

A’s gain = 20%

∴ A’s cost price = Rs 1800 100

100 20

×

+ = Rs

1800 100

120

× = Rs 1500

Hence, A will pay Rs 1500 for bicycle.

35. Roma sold a watch to Monu at 12% gain and Monu had to sell it to

Lavish at a loss 5%. If Lavish paid Rs 1330, how much did Roma

pay for it?

Ans. Let cost price of the watch by ‘Roma’ be Rs x

Profit = 12% of x = 12 3

100 25

xx× =

Selling price of the watch by ‘Roma’ = 3

25

xx + =

25 3 28

25 25

x x x+=

∴ Cost price of the watch by ‘Monu’ = 28

25

x

Loss = 5% of 28 5 28 7

25 100 25 125

x x x= × =

Selling price of the watch by ‘Monu’ = 28 7

25 125

x x−

= 140 7 133

125 125

x x x−=

∴ Cost price of the watch by ‘Lavish’ = 133

125

x

Thus,133

1330,125

x=

1330 125

133x

×=

∴ x = 1250

Hence, cost price of the watch for Roma is Rs 1250.

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36. Dhani Ram purchased a cow for Rs 6000 and a buffalo for

Rs 12000. He sold the buffalo at a profit of 15% and the cow at a

loss of 10%. Calculate his overall profit or loss percentage.

Ans. Cost price of cow = Rs 6000

and cost price of buffalo = Rs 12000

Thus, total cost price of cow and buffalo = Rs (6000 + 12000)

= Rs 18000

Dhani Ram sold the cow at the loss of 10%, then selling price of cow

= 10

1100

−

of (cost price of cow)

= Rs 10

1 6000100

− ×

= Rs

906000

100×

= Rs 90 × 60 = Rs 5400

Dhani Ram sold the buffalo at the profit of 15%

then, Selling price of buffalo = 15

1100

+

of (cost price of buffalo)

= Rs 15

1 12000100

+ ×

= Rs 115

12000100

×

= Rs 115 × 120 = Rs 13800

∴ Selling price of cow and buffalo = Rs (5400 + 13800)

= Rs 19200

Thus, profit = selling price – cost price

= Rs (19200 – 18000) = Rs 1200

Hence, profit% = Profit

100 %Cost price

×

= 1200

100 %18000

×

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= 1200 120 20 2

% % % 6 %180 18 3 3

= = =

Hence, overall percentage of Dhani Ram is 2

6 %3

.

37. By selling an almirah for Rs 3920, a shopkeeper would gain 12%. If

it is sold for Rs 4375, find his gain or loss percentage.

Ans. When selling price of almirah = Rs 3920 and gain = 12%

then cost price P = ?

We know that, selling price, SP = 12

1100

+

of CP

⇒ Rs 3920 = 100 12

100

+

of CP

⇒ CP = Rs 3920

100112

×

= Rs 35 × 100 = Rs 3500

When cost price of almirah = Rs 3500

and selling price of almirah = Rs 4375

Then, gain = SP – CP = Rs (4375 – 3500) = Rs 875

Hence, gain% = gain

100 %CP

×

= 875 875

100 % % 25%3500 35

× = =

38. By selling a bicycle at Rs 1334, a shopkeeper would suffer a loss of

8%. At how much amount should he sell it to make a profit of

112 %

2?

Ans. Selling price of bicycle = Rs 1334

Shopkeeper would suffer a loss % = 8%

Cost price = ?

we know that selling price = (1– loss%) of CP

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⇒ Rs 1334 = 8

1 CP100

− ×

⇒ Cost price of bicycle = Rs 1334

10092

×

⇒ Cost price of bicycle = Rs 1334

2523

×

⇒ Cost price of bicycle CP = Rs 58 × 25 = Rs 1450

Now, CP = Rs 1450

Profit on bicycle = 1 25

12 %2% 2

=

Selling price of bicycle = 25

1 CP2 100

+ ×

×

⇒ Selling price of bicycle = 25

12 100

+

× × (Rs 1450)


1 14508

+ ×


14508

×

⇒ Selling price of bicycle = (9 × 181.25) = Rs 1631.25

39. Sohan bought a certain number of note-books for Rs 600. He sold

1

4 of them at 5 per cent loss. At what price should he sell the

remaining note-books so as to gain 10% on the whole?

Ans.

Cost price of note-books = Rs 600

Gain desired on the whole = 10%

Then total selling price of all the note-books

= ( )100 gain% 100 10

CP100 100

+ + × =

× Rs 600

= Rs 110

600100

× = Rs 660

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Cost price of 1

4 of the books =

1

4× Rs 600 = Rs 150

Loss on these note-books = 5%

Then, selling price of these note-books

= ( )100 Loss %

100

−× CP =

( )100 5

100

−× Rs 150

= Rs 95

150100

× = Rs 14250

100 = Rs 142.50

Thus, required selling price of the remaining note-books

= Rs(660 – 142.50) = Rs 517.50

40. Sanjay sold a bicycle at 5% profit. If the cost had been 30% less and

the selling price Rs 63 less, he would have made a profit of 30%.

What is the cost price of the bicycle?

Ans. Let cost price of the bicycle = Rs 100

When profit = 5% ;

S.P. = Rs (100 + 5) = Rs 105

New cost price = 30

100 100100

− ×

= Rs (100 – 30) = Rs 70

Profit on bicycle = 30%

Thus selling price = ( )100 Profit

100

+ × cost price

= ( )100 30

100

+ × Rs 70 =

130

100 × Rs 70

= Rs 130 70

100

× = Rs 91

Thus, difference of two selling prices = Rs (105 – 91) = Rs 14

If difference is Rs 14 then cost price of the bicycle = Rs 100

If difference is Rs 1 then cost price of bicycle = Rs 100

14

If difference is Rs 63 then cost price of bicycle = Rs 100 63

14

×

= Rs 50 × 9 = Rs 450.

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41. Mona sold a pressure cooker at a loss of 8%. Had she bought it at10% less and sold for Rs 88 more, she would have gained 20%.Find the cost price of the pressure cooker.

Ans. Let the cost price of pressure cooker = Rs 100

loss on pressure cooker = 8%

Then, selling price of pressure cooker = Rs (100 – 8) = Rs 92

Again, cost price of pressure cooker = Rs (100 – 10) = Rs 90

gain = 20%

Thus, selling price of pressure cooker = C.P. (100 gain%)

100

× +

= Rs 90(100 20)

100

+

= Rs 90 120

100

× = Rs 108

∴ Difference in two selling prices (108 – 92) = Rs 16

If difference is Rs 16, then cost price = Rs 100

and if difference is Rs 88, then cost price = 100 88

16

× = Rs 550

Hence, cost price of pressure cooker is Rs 550.

42. The manufacturing price of a T.V. set was Rs 5000. The companysold it to a distributor at 16% profit. The distributor sold it to adealer at 10% profit. The dealer sold it to a customer at 20% profit.Find the price the customer paid.

Ans. The manufacturing price of T.V. set = Rs 5000

Profit = 16%

Selling price of T.V. set = 16

1100

+

of Rs 5000

= 100 16

100

+

of Rs 5000

= 116

100 × Rs 5000 = Rs

116

100 × 5000

= Rs 116 × 50 = Rs 5800

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Thus, cost price of T.V. set for distributor = Rs 5800

Now, Profit = 10%

Selling price of T.V. set for distributor

= 10

1100

+

of Rs 5800

= 10

1100

+

of Rs 5800 = Rs

1105800

100×

= Rs 110 × 58 = Rs 6380

Thus, cost price of T.V. set for dealer = Rs 6380

Again profit = 20%

Selling price of T.V. set for dealer

= 20

1100

+

of Rs 6380

= 100 20

100

+

of Rs 6380

= 120

100 of Rs 6380 = Rs

1206380

100×

= Rs 12 × 638 = Rs 7656

Hence, the price the customer paid = Rs 7656.

43. A sells an article to B at a profit of 20% and B sells it to C at a loss of

6%. If C pays Rs 846, find how much did A pay for it.

Ans. Let the amount A pays for the article be x

when A sells to B at a profit of 20%

Then, cost price for B or the selling price for A = 20

1100

+

cost

price for A.

= 2

110

+

× Rs x = Rs

12

10x× = Rs

12

10

x

i.e. cost price of the article for B = Rs 12

10

x

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But, B sells to C at a loss of 6%

Then, cost price for C or the selling price for B

= 6

1100

−

of cost price for B =

61

100

−

of Rs

12

10

x

= 3

150

−

of Rs

12

10

x = Rs

47 12

50 10

x× = Rs

564

500

x

But, C pays Rs 846, for an article then, 564

500x = Rs 846

⇒ x = Rs 500

846564

× = Rs 250

846282

×

= Rs 3 × 250 = Rs 750

Hence, cost price of an article for A = Rs 750

44. Saurav sold an article at a profit of 12%. Had it been sold for

Rs 16 more, the profit would have been 20%. Find, the selling price

of the article.

Ans. Let the selling price of an article be Rs x,

Then, profit on article = 12%

∴ Selling price = 1100

P +

of cost price

∴ Rs x = 12

1100

+

of cost price

= 112

100

of cost price

⇒ Cost price = Rs 100

112 × x =

100

112

x

To make 20% profit,

Selling price = 20

1100

+

of cost price

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= 1

15

+

of cost price =

6

5of cost price

= 6

5of Rs

100

112

x = Rs

6 100

5 112

x ×

= Rs 6 20

112

x×

= Rs 120

112x

As per condition,

120

112x = x + 16 ⇒

120

112x x− = 16

⇒120 112

112

x x− = 16 ⇒

8

112

x = 16

⇒ Rs 16 112

8

× = Rs 2 × 112 = Rs 224

Hence, the selling price of the article is Rs 224.

45. After allowing a discount of 15% a navycut was sold for Rs 578.

Find its marked price.

Ans. Let market price of the navycut be Rs x.

Discount = 15% of Rs x = Rs 15

100x× = Rs

15

100

x = Rs

3

20

x

Selling price of the navycut = Rs 3

20

xx

−

= Rs 20 3

20

x x−

= Rs 17

20

x

∴17

20

x = 578 ⇒ x =

578 20

17

×⇒ x = 680.

Hence, market price of the navycut is Rs 680.

46. A coat was bought for Rs 435 after getting a discount of 13%. Find

the marked price of the coat.

Ans. Let marked price of the coat be Rs x

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Discount = 13% of Rs x

= Rs 13

100x× = Rs

13

100

x

Then, selling price of the coat = Rs 13

100

xx

−

= Rs 100 13

100

x x−

= Rs 87

100

x

87

100

x = 435 ⇒ x =

435 100

87

× ⇒ x = 500

Hence, marked price of the coat is Rs 500.

47. A shopkeeper buys a Tea set for Rs 1200 and marks it 80% above the

cost price. If he gives 15% discount on it, find:

(i) the marked price

(ii) the selling price

(iii) his profit percentage

Ans. (i) Cost price of a tea set = Rs 1200

Marked price of tea set

= Rs1200 + 80% of (Rs 1200)

= Rs 80

1200 1200100

+ ×

= Rs [1200 + 80 × 12]

= Rs [1200 + 960] = Rs 2160

(ii) Marked price = Rs 2160, discount = 15%

Selling price = ?

Selling price = 1100

d −

of marked price

Selling price = 15

1100

−

× Rs 2160

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Selling price = Rs 85

2160100

×

Selling price = Rs 17

216020

×

Selling price = Rs 17 × 108 = Rs 1836

(iii) Profit = selling price – cost price

= Rs (1836 – 1200) = Rs 636

Profit % = Profit

100 %Cost price

×

= 636

100 %1200

×

=

636%

12 = 53%

48. The cost price of a Reliance mobile is Rs 1600, which is 20% below

the marked price. If the article is sold at a discount of 16%, find:

(i) the marked price

(ii) the selling price

(iii) profit percentage.

Ans. (i) Cost price of Reliance mobile = Rs 1600

Since the cost price of Reliance mobile is 20% below the marked

price.

Let the marked price of Reliance mobile = Rs x

Then, Cost price = Marked price – 20% of Marked price

⇒ Rs 1600 = x – 20% of x

⇒ Rs 1600 = 20

100x x− ×

⇒ Rs 1600 = 80

100

x

⇒ x = Rs 100

160080

×

= Rs 20 × 100 = Rs 2000

Hence, the marked price of Reliance mobile = Rs 2000

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(ii) Marked price of Reliance mobile = Rs 2000, discount = 16%,

Selling price = ?

Selling price = 16

1100

−

of marked price

= 100 16

100

−

of Rs 2000

= Rs 84

2000100

× = Rs 84 × 20 = 1680

(iii) Profit = selling price – cost price = Rs (1680 – 1600) = Rs 80

Hence, Profit % = Profit

100 %Cost price

×

= 80

100 %1600

×

=

80%

16 = 5%.

49. An umbrella was marked 40% above cost price and a discount of

35% was given on its marked price. Find the gain or loss per cent

made by the shopkeeper.

Ans. Let cost price of the umbrella be Rs x.

Marked price of the umbrella = Rs (x + 40% of x)

= Rs 40

100x x

+ ×

= Rs 2

5

xx

+

= Rs 5 2

5

x x+

= Rs 7

5

x

Discount on umbrella = 35% of Rs 7

5

x

= Rs 35

100 ×

7

5

x = Rs

49

100

x

Thus, selling price of the umbrella = Rs 7 49

–5 100

x x

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= Rs 140 – 49

100

x x

= Rs 91

100

x

Loss = Rs 91

–100

xx

= Rs 100 – 91

100

x x = Rs

9

100

x

Hence, Loss% = 9

100

x

x× × 100% = 9%

50. Mr Kabuliwala purchased a washing machine for Rs 7660. After

allowing a discount of 12% on its marked price he sells it at a gain

of 10%. Find the marked price.

Ans. Let marked price of the washing machine be Rs x.

Discount = 12% of Rs x = Rs 12

100 × x = Rs

3

25

x

Thus, selling price of the washing machine

= Rs 3

–25

xx

= Rs 25 – 3

25

x x

= Rs 22

25

x

Cost price of the washing machine = Rs 7660

Gain = 10%

Thus, selling price of the washing machine

= Rs 100 10

100

+ × 7660 = Rs

110

100 × 7660 = Rs 8426

If selling price Rs 22

25

x, then marked price = Rs x

If selling price Re 1, then marked price = Rs 25

22

x

x

×

If selling price Rs 8426, then marked price = Rs 25

22 × 8426

= Rs 9575

51. Find a single discount equivalent to two successive discounts of40% and 5%.

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Ans. Let marked price = Rs 100

Rate of first discount = 40%

and rate of second discount = 5%

Thus, selling price = marked price × (100 – discount%)

100

= 100 (100 – 40) (100 – 5)

100 100

× ×

×

= 100 60 95

100 100

× ×

× = Rs 57

Thus, total discount = Rs (100 – 57) = Rs 43

Hence, rate of single discount is 43%

52. Find a single discount equivalent to three successive discounts of

20%, 5% and 1%.

Ans. Let marked price = Rs 100

Rate of first discount = 20%

Rate of second discount = 5%

Rate of third discount = 1%

∴ Selling price = marked price (100 – discount%)

100

×

= 100(100 – 20) (100 – 5) (100 –1)

100 100 100

× ×

× ×

= 100 80 95 99

100 100 100

× × ×

× × =

7524

100 = Rs 75.24

Thus, total amount of discount = Rs (100 – 75.24) = Rs 24.76

Hence, single discount = 24.76%.

53. If after giving a discount of 10%, a shopkeeper still makes a profit of

12.5%, find how much above the cost price he had marked the prices.

Ans. Let the cost price of the article be Rs x.

Profit is 12.5%

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Selling price of article = 12.5

1100

+

of Rs x

= 100 12.5

100

+

of Rs x = Rs 112.5

100x

Shopkeeper allows a discount of 10%

Selling price = 10

1–100

of marked price

⇒112.5

100

x=

90

100 of marked price

⇒112.5

100

x=

9

10 of marked price

⇒ Marked price = 10

9 ×

112.5

100

x

= 1

9 ×

112.5

10

x =

112.5

90x

Thus, the excess value to be marked = marked price – cost price

= Rs 112.5

90

x – Rs x = Rs

112.5–

90

xx

= Rs 112.5 – 90

90

x x

= Rs 22.5

90

x

Thus, the percentage of excess value to be marked

= excess value

100 %cost price

×

=

22.5

90 100 %

x

x

×

= 22.5

100 %90

×

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= 225

%9

= 25%

Hence, the shopkeeper marks the article above the cost price by 25%.

54. If a shopkeeper marks his goods at 20% above the cost price and

then gives 20% discount, find his gain or loss percentage.

Ans. Let the cost price of an article be Rs x.

Since the dealer marks his goods 20% above the cost price.

Marked price = Cost price + 20% of Cost price

= Rs x + 20

100 of Rs x = Rs

20

100

xx

+

= Rs 120

100

x = Rs

6

5

x

Selling price = 1–100

d

of Marked price

= 20

1–100

of Rs 6

5

x = Rs

80

100 ×

6

5

x = Rs

96

100

x

Loss = cost price – selling price

= Rs x – Rs 96

100

x = Rs

96–

100

xx

= Rs 100 – 96

100

x x

= Rs 4

100

x = Rs

25

x

Loss% = Loss

100 %Cost price

×

= 25 100 %

x

x

×

= 100 %25

x

x

×

× =

100%

25

= 4%

© EDULABZ

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55. After allowing a discount of 10% on the marked price of an article, a

shopkeeper still makes a profit of 17%. By what percent is the marked

price above the cost price?

Ans. Let the cost price of the article be Rs x.

Profit is 17%

Selling price = 1100

P +

of Cost price

= 17

1100

+

of Rs x = Rs

117

100x

Since the dealer allows a discount of 10%

Selling price = 10

1–100

of Marked price

⇒ Rs 117

100

x=

90

100 of Marked price

⇒ Rs 117

100

x=

9

10 of Marked price

⇒ Marked price = Rs 117

100 ×

10

9 = Rs

13

10x

Thus, the excess value to be marked

= Marked price – Cost price

= Rs 13

10

x – Rs x = Rs

13–

10

xx

= Rs 3

10

x

Thus, the percentage of excess value to be marked

= excess value

100 %cost price

×

=

3

10 100 %

x

x

×

= 3

10

x

x× × 100

Percentage-Profit and Loss - Testlabz©EDULABZ INTERNA TIONAL Math Class VIII 5 Question Bank Amount...

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Transcript of Percentage-Profit and Loss - Testlabz©EDULABZ INTERNA TIONAL Math Class VIII 5 Question Bank Amount...