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S.chand Class 8 Maths Solution Chapter 8 Percentage And Its Applications Exercise 8 E

Exercise 8 E

Question 1

1. Rajendra purchases a pair of chappals from a Bata Shop worth $₹ 99.95$. The rate of sales tax is $7 \%$. Calculate the total amount to be paid by him.

2. A steel almirah is quoted at $₹ 1100$. Sales tax at the rate of $7 \%$ is charged extra. Find the amount the buyer has to pay for the almirah.

3. Vinay paid $₹ 24.50$ as sales tax on a pair of shoes worth $₹ 350$. Find the rate of sales tax.

4. Rachna paid $₹ 5665$ for a colour television. If the sales tax is charged at the rate of $10 \%$ on the list price of the T.V., find the list price of the T.V.

5. Radha went to a departmental store and purchased the following articles :

(a) Bakery products (S.T. @ 10\%) worth ₹ 42 ;

(b) Clothes (S.T. 7\%) worth ₹ 800 ;

(d) Cosmetics (S.T. 10\%) worth ₹ 150 .

Find the amount she has to pay for the bill.

6. Ranjeeta purchased a set of cosmetics. She paid $₹ 165$ for it including sales tax. If the rate of sales tax is $10 \%$, find the list price of the set.

7. Seema bought a refrigerator for $₹ 14,300$ including a VAT of $10 \%$. Find the price of the refrigerator before VAT was added.

8. Mr. Sinha purchased a scooter for $₹ 48,505$ including $9 \%$ VAT. Find the original price of the scooter without VAT.

9. A bicycle manufacturer sells a bicycle at $₹ 1308$ after adding the VAT at the rate of $9 \%$. Still he makes a profit of $20 \%$ on the sale of each bicycle. What is the manufacturing cost of each bicycle.

Multiple Choice Questions (MCQs)

10. The total bill for a sewing machine is $₹ 872$. If the shopkeeper charges $9 \%$ S.T. on the list price of the sewing machine, find the list price of the sewing machine.

(a) ₹ 750

(b) ₹ 850

(d) ₹ 840

11. Vikrant buys crockery worth ₹ 6500 . He gets a rebate of $3 \%$ on the bill. If sales tax@ $5 \%$ is charged, find the amount he will have to pay for the bill.

(a) ₹ $6062.25$

(b) ₹ $6602.25$

(d) ₹ $6206.25$

S.chand Class 8 Maths Solution Chapter 8 Percentage And Its Applications Exercise 8 D

Exercise 8 D

Question 1

1. Find the discount and the amount actually paid if

(a) A shirt having a price tag of $₹ 600$ is sold at $15 \%$ discount.

(b) A vacuum cleaner with a marked price of $₹ 6000$ is sold at a discount of $5 \%$ on immediate cash payment.

2. Find the S.P. when M.P. $=₹ 1500$ and discount $=12 \%$.

3. Find the rate of discount when

(i) M.P. $=₹ 300$ and S.P. $=₹ 240$

(ii) M.P. $=₹ 2800$ and S.P. $=₹ 2100$

4. Find the M.P. when

(i) S.P. $=₹ 1900$ and discount $=5 \%$

(ii) S.P. $=₹ 4200$ and discount $=16 \%$

5. A shopkeeper marks his goods $30 \%$ above the cost price and gives a discount of $15 \%$ on the marked price. What gain $\%$ does he make ?

6. A watch dealer pays $10 \%$ custom duty on a watch which costs ₹ 500 abroad. For how should much he mark it, if he desires to make a profit of $20 \%$ after giving a discount of $25 \%$ to the buyer ?

7. A shopkeeper allows a cash discount of $12.5 \%$ on a machine. A customer pays an amount of $₹ 437.50$ for a machine. At what price is the machine listed ?

8. A shopkeeper offers $10 \%$ off-season discount to the customers and still makes a profit of $26 \%$. What is the cost price of a pair of shoes marked at $₹ 1120$ ?

9. Naseem runs a readymade garments shop. He marks the garments at such a price that even after allowing a discount of $12.5 \%$, he makes a profit of $10 \%$. Find the marked price of a suit which costs him $₹ 1470$.

10. A shopkeeper buys an article for $₹ 400$ and marks it for sale at a price that may give him $80 \%$ profit on his cost. He, however gives $15 \%$ discount on the marked price to his customer.

Calculate :

(i) the marked price of the article,

(ii) the discount in rupees given to the customer,

(iii) the actual percentage profit made by the shopkeeper.

11. When a discount of $15 \%$ is allowed on the marked price of an article, it is sold for $₹ 2975$.

(i) Calculate its marked price. Given that the marked price is $40 \%$ above the cost price of the article, calculate :

(ii) its cost price

(iii) the profit in $₹$ made by the sale of the article.

12. A shopkeeper allows a discount of $20 \%$ on the marked price of an article, and sells it for $₹ 896$.

(a) Calculate the marked price of the article.

(b) By selling the article at the discounted price if he still gains $12 \%$ on his cost price, what was the cost price ?

13. A sells a car priced at $₹ 36,000$. He gives a discount of $8 \%$ on the first $₹ 20,000$ and $5 \%$ on remaining $₹ 16,000 . B$ also sells a car of the same make priced at $₹ 36,000$. He gives a discount of $7 \%$ on the total price. Calculate the actual price charged by $A$ and $B$ for the cars.

14. A dealer of scientific instruments allows $20 \%$ discount on the marked price of the instruments and still makes a profit of $25 \%$. If his gain over the sale of a instrument is $₹ 150$, find the marked price of the instruments.

15. A washing machine is marked at $₹ 7500$. The dealer allows successive discounts of $8 \%, 5 \%$ and $2 \%$ on it. What is the net selling price?

16. After allowing two successive discounts of $15 \%$ and $5 \%$, a fan is sold for $₹ 2907$. What is the marked price of the fan?

Multiple Choice Questions (MCQs)

17. A shopkeeper carns $15 \%$ profit on a shirt even after allowing $31 \%$ discount on the marked price. If the marked price is $₹ 1250$, then the cost price of the shirt is

(a) 2870

(b) $₹ 800$

(d) ₹ 690

18. Two successive discount of $10 \%$ and $5 \%$ are cqual to a single discount of

(a) $15 \%$

(b) $7 \frac{1}{2} \%$

(d) $14 \frac{1}{2} \%$

High Order Thinking Skills (HOTS)

19. Applied to a bill to $₹ 15000$, what is the difference in rupees between a discount of $50 \%$ and two successive discounts of $30 \%$ and $20 \%$ ?

S.chand Class 8 Maths Solution Chapter 8 Percentage And Its Applications Exercise 8 C

Exercise 8 C

Question 1

1. Kamal bought paper sheets for $₹ 7200$ and spent $₹ 200$ on transport. Paying $₹ 600$, he had 330 boxes made, which he sold at $₹ 28$ each. Find his total profit and profit $\%$.

2. A man buys a T.V for $₹ 6800$. For how much should he sell it so as to (i) gain $10 \%$, (ii) lose $5 \%$ on it ?

3. By selling a radio for $₹ 528$, Mohit gains $10 \%$. Find his cost price.

4. A watch sold for $₹ 448$ gives a profit of only $12 \%$. Find the profit $\%$ if the selling price had been $₹ 512$.

5. Prem sold a transistor to Sudhir at a gain of $10 \%$ and Sudhir sold it to Hari at a gain of $15 \%$. Prem had bought it for $₹ 500$, what did it cost to Hari ?

6. A manufacturer sells an article to a wholesaler at a profit of $18 \%$, the wholesaler sells it to a retailer at a profit of $20 \%$. The retailer sells it to a customer at a profit of $25 \%$. If the customer pays $₹ 30.09$ for it, find the cost of the manufacturer.

7. A shopkeeper sold an article at a gain of $5 \%$. If he had sold it for $₹ 16.50$ less, he would have lost $5 \%$. Find the cost price of the article.

8. By selling a stool for $₹ 67.50$, a carpenter loses $10 \%$. How much per cent would he gain or lose by selling it for $₹ 82.50$ ?

9. By selling a purse for $₹ 250$, Ranjana loses one-sixth of what it cost her. Find

(i) the cost price of the purse

(ii) her loss percentage.

10. If the cost price of 11 shirts is equal to the selling price of 10 shirts, find the percentage profit or loss.

11. Pens are bought at 12 for a rupee and sold at 9 for a rupee. Find the gain\%.

12. By selling 100 mangoes, a fruit seller gains the S.P. of 20 mangoes. Find his gain\%.

13. By selling 144 hens, Mala lost the S.P. of 6 hens. Find her loss $\%$.

14. A shopkeeper sold two pairs of jeans for $₹ 720$ each, gaining $20 \%$ on one and losing $20 \%$ on the other. Find his gain or loss $\%$.

15. John bought two horses at $₹ 20,000$ each. He sold one horse at $15 \%$ gain. But he had to sell the second horse at a loss. If he had sufferred a loss of $₹ 1800$ on the whole transaction, find the selling price of the second horse.

16. A shopkeeper buys two T.V. sets of the same type. He sells one of them at a profit of $20 \%$ and the other at a loss of $5 \%$. If the difference in selling prices is $₹ 700$, find the cost price of each T.V. set.

17. A publisher sells a book for $₹ 168$ at a profit of $20 \%$. If his cost of production increases by $30 \%$, what should be the increase in the price of the book so that his percentage profit remains the same ?

18. The difference in prices when a commodity is sold at a profit of $4 \%$ and at a profit of $6 \%$ is $₹ 3$. Find the selling prices of the commodity in the two cases.

19. A man buys a plot of land at ₹ $3,60,000$. He sells one third of the plot at a loss of $20 \%$. Again, he sells two -thirds of the plot left at a profit of $25 \%$. At what price should he sell the remaining plot in order to get a profit of $10 \%$ on the whole ?

20. A shopkeeper bought locks at the rate of 8 locks for $₹ 34$ and sold them at the rate of 12 locks for $₹ 57$. Calculate:

(i) his gain per cent, and

(ii) the number of locks he should sell to earn a profit of $₹ 45$.

[Hint. Let the number of locks bought be the LCM of 8 and 12]

21. Dinesh sold his motorcycle to Naveen at a loss of $28 \%$. Naveen spent $₹ 1680$ on its repairs and sold the motorcycle to Saran for ₹ 35,910 making a profit of $12.5 \%$. Find the cost of the motor cycle for Dinesh.

22. The C.P. of two watches taken together is $₹ 840$. If by selling one at a profit of $16 \%$ and the other at a loss of $12 \%$, there is no gain or loss in the whole transaction then find the C.P. of each watch.

Multiple Choice Questions (MCQs)

23. Ramesh owns a plot worth $₹ 10,000$. He sells it to Mukesh at a profit of $10 \%$. After sometime, Mukesh sells it back to Ramesh at a loss of $10 \%$, then what is Ramesh's total gain or loss?

(a) loses ₹ 100

(b) loses ₹ 900

(d) gains ₹ 1100

24. If $5 \%$ more is gained by selling an article for $₹ 350$ than by selling it for $₹ 340$, then the cost of the article is:

(a) ₹ 50

(b) ₹ 160

(d) $₹ 225$

High Order Thinking Skills (HOTS)

25. Some toffees are bought at the rate of 11 for $₹ 10$ and the same number at the rate of 9 for $₹ 10$. If the whole lot is sold at one rupee per toffee, find the gain or loss in the whole transaction.

[Hint. Let the number of toffees bought be the LCM of 11 and 9.]

S.chand Class 8 Maths Solution Chapter 8 Percentage And Its Applications Exercise 8 B

Exercise 8 B

Question 1

1. A man whose income is $₹ 576$ a year spends $₹ 432$ a year. What percentage of his income does he save ?

2. If $70 \%$ of the students in a school are boys and the number of girls is 540 , find the number of boys in the school?

3. An alloy consists of 13 parts of copper to 7 parts of zinc and 5 parts of nickel. What is the percentage composition of the alloy?

4. The population of a town increases by $10 \%$ annually. If the present population is 22000 , find its population a year ago.

5. Manoj's income increased by $20 \%$ and then decreased by $20 \%$. What is the total percentage change in Manoj's income?

6. In an examination Piyush scored 490 marks. If he scored $70 \%$ marks, find the maximum marks.

7. Calculations show that an angle is $37 \frac{1}{2}^{\circ}$. The size obtained by drawing and measurement is $35^{\circ}$. Find the error per cent.

8. Chalk contains $10 \%$ calcium, $3 \%$ carbon and $12 \%$ oxygen. Find the amount (in grams) of each of these compounds in $1 \mathrm{~kg}$ of chalk.

9. A candidate scored $25 \%$ marks in an examination and failed by 30 marks, while another candidate who scored $50 \%$ marks got 20 marks more than the minimum pass marks. Find the maximum marks and minimum pass marks.

10. There are 120 girls and 57 boys in a school. If $5 \%$ of the girls leave and no new pupils are admitted, what percentage of the whole school will be boys ?

11. In an election, a candidate got $65 \%$ of the total valid votes. $8 \%$ of the total votes were declared invalid. If the total number of votes cast was $6,00,000$, find the number of valid votes polled in favour of the candidate.

12. The sides of a rectangle are $20 \mathrm{~cm}$ and $15 \mathrm{~cm}$. If each side of the rectangle is increased by $20 \%$, find the percentage increase in the area.

13. In an examination 2500 students appeared out of which 1100 were girls. $50 \%$ of the boys and $40 \%$ of the girls passed the examination. What percentage of the candidates failed in the examination?

Multiple Choice Questions (MCQs)

14. Rita invested $25 \%$ more than Sunil. Sunil invested $30 \%$ less than Abhinav who invested $₹ 6000$. What is the respective ratio between the amount that Rita invested and the total amount invested by all of them together ?

(a) $35: 104$

(b) $13: 29$

(d) $35: 103$

15. Raja got $76 \%$ marks and Seema got 480 marks in a test. The maximum marks of the test is equal to the marks obtained by Raja and Seema together. How many marks did Raja score in the test ?

(a) 1450

(b) 1520

(d) 2000

High Order Thinking Skills (HOTS)

16. A father gives $1 \%$ of his monthly income to his two sons as pocket money. The elder son gets $80 \%$ of the total amount of money given and he spends $80 \%$ of his share. If he saves ₹ 20 per month, determine father's monthly income.

(a) ₹ 10,000

(b) ₹ 12,000

(d) ₹ 15,000

S.chand Class 8 Maths Solution Chapter 8 Percentage And Its Applications Exercise 8 A

Exercise 8 A

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Question 1

Write these percentages as fractions and decimals :

(i) $60 \%$

Sol :

$=\dfrac{60}{100}=\dfrac{3}{5}$

=0.6

(ii) $240 \%$

Sol :

$=\dfrac{240}{100}=\dfrac{12}{5}$

=2.4

(iii) $12 \dfrac{1}{2} \%$

Sol :

$=\dfrac{25}{2}\%=\dfrac{25}{2 \times 100}$

$=\dfrac{1}{8}$

=0.125

(iv) $55 \dfrac{2}{3} \%$

Sol :

$=\dfrac{167}{3}\%$

$=\dfrac{167}{3 \times 100}=\dfrac{167}{300}$

=0.557...

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Question 2

Write these numbers as percentages :

(i) $\frac{3}{4}$Sol :

Sol :

$=\dfrac{3}{4} \times 100$

=75%

(ii) $\frac{21}{40}$Sol :

Sol :

$=\dfrac{21}{40} \times 100$

$=\dfrac{105}{2}\%$

$=52\dfrac{1}{2}\%$

(iii) $0.008$

Sol :

$=\dfrac{8}{1000} \times 100$

$=\dfrac{4}{5}\%$

=0.8%

(iv) $0.375$

Sol :

$=\dfrac{375}{1000}\times 100$

$=\dfrac{75}{2}\%$

=37.5%

(v) $1.07$

Sol :

$=\dfrac{107}{100} \times 100$

=107 %

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Question 3

Express the following percentage as ratios:

(i) $200 \%$

Sol :

$=\dfrac{200}{100}=\dfrac{2}{1}$

=2 : 1

(ii) $6 \dfrac{2}{3} \%$

Sol :

$=\dfrac{20}{3}\%=\dfrac{20}{3 \times 100}$

$=\dfrac{1}{15}$

=1 : 15

(iii) $75 \%$

Sol :

$=\dfrac{75}{100}=\dfrac{3}{4}$

=3 : 4

(iv) $33 \dfrac{1}{3} \%$

Sol :

$=\dfrac{100}{3}\%=\dfrac{100}{3 \times 100}$

$=\dfrac{1}{3}$

=1 : 3

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Question 4

Express the following ratios as percentage:

(i) $1: 2$

Sol :

$=\dfrac{1}{2} \times 100$

=50%

(ii) $7: 10$

Sol :

$=\dfrac{7}{10} \times 100$

=70%

(iii) $21: 25$

Sol :

$=\dfrac{21}{25} \times 100$

=84%

(iv) $5: 12$

Sol :

$=\dfrac{5}{12} \times 100$

$=\dfrac{125}{3}\%=41\dfrac{2}{3}\%$

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Question 5

Evaluate :

(i) $19 \%$ of $₹ 4200$

Sol :

$=\dfrac{19}{100} \times 4200$

=798 g

(ii) $75 \%$ of $440 \mathrm{~kg}$

Sol :

$=\dfrac{75}{100} \times 440$

=330 g

(iii) $30 \%$ of $20 \mathrm{~g}$

Sol :

$=\dfrac{30}{100} \times 20$

=6 g

(iv) $2.5 \%$ of $350 \mathrm{~m}$

Sol :

$=\dfrac{25}{10 \times 100} \times 350$

$=\dfrac{35}{4}$

=8.75 m

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Question 6

Express the first quantity as a percentage of the second :

(i) $20 \mathrm{~g}$ of $4 \mathrm{~kg}$

Sol :

=20 g of 4000g

$=\dfrac{20}{4000} \times 100$

$=\dfrac{1}{2}\%$

=0.5%

(ii) $200 \mathrm{~mL}$ of 5 litres

Sol :

=200 ml of 5000 ml

$=\dfrac{200}{5000} \times 100$

=4%

(iii) $48 \mathrm{~cm}$ of $1 \mathrm{~m}$

Sol :

=48 cm pf 100 cm

$=\dfrac{48}{100} \times 100$

=48%

(iv) $\frac{2}{3}$ of $\frac{1}{2}$

Sol :

$=\dfrac{\frac{2}{3}}{\frac{1}{3}} \times 100$

$=\dfrac{2}{3} \times \dfrac{3}{1} \times 100$

=200 %

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Question 7

(i) If $14 \%$ of a certain number is 63 , find the number.

Sol :

Let the required number be x

14% of x=63

$\dfrac{14}{100} \times x=63$

$x=\dfrac{63 \times 100}{14}$

x=450

(ii) If $12 \frac{1}{2} \%$ of a certain amount is $₹ 62.50$, find the amount.

Sol :

Let the amount be x

$12 \frac{1}{2} \%$ of x=62.50

$\dfrac{25}{2}\% \times x$=62.50

$\dfrac{25}{2\times 100} \times x$=62.50

$x=\dfrac{62.50}{100} \times \dfrac{2}{25} \times 100$

x=500

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Question 8

There were 4200 people at a concert and 1400 of these were female. What percentage were male ?

Sol :

Total number of people=4200

Number of female=1400

Number of male=4200-1400=2800

Percentage of male $\dfrac{2800}{4200} \times 100$

$=\dfrac{200}{3} \%=66\dfrac{2}{3}\%$

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Question 9

The cost of a theatre ticket is increased by $40 \%$ for a special movie. What is the new price if the normal price was ₹ 160.

Sol :

Normal price was ₹ 160

Increase =40% of 160$

$=\dfrac{40}{100} \times 160$

=4×16=64

New price=160+64=224

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Question 10

A motorcycle originally cost $₹ 40,000$. Its cost has decreased by $22 \%$. What is its cost now ?

Sol :

Original cost of motorcycle=40000

Decrease=22% of 40000

$=\dfrac{22}{100} \times 40000$

=22×400=8800

New cost=40000-8800=31200

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Question 11

The price of a garment has been reduced by $15 \%$ in a sale to $₹ 306$. Find its original price.

Sol :

Let the original cost be x

According to question,

x-15% of x=306

$x-\dfrac{15}{100}\times x=306$

$x-\dfrac{3x}{20}=306$

$\dfrac{20x-3x}{20}=306$

$\dfrac{17x}{20}=306$

$x=\dfrac{306 \times 20}{17}$

x=360

Multiple Choice Questions (MCQs)

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Question 12

What percent of $\sqrt{0.0169}$ is $0.0117$ ?

(a) 0.9

(b) 0.1

(c) 0.09

(d) 9

Sol :

x% of $\sqrt{0.0169}=0.0117$

$\dfrac{x}{100} \times \sqrt{\dfrac{169}{10000}}=\dfrac{117}{10000}$

$\dfrac{x}{100} \times \dfrac{13}{100}=\dfrac{117}{10000}$

$x \times 13=\dfrac{117}{10000} \times 100 \times 100$

$x=\dfrac{117}{13}$

x=9

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Question 13

What per cent is $3 \%$ of $5 \%$ ?

(a) $15 \%$

(b) $30 \%$

(c) $50 \%$

(d) $60 \%$

Sol :

Let the value be 100

x% of 5%=3%

$\dfrac{x}{100} \times \dfrac{5}{100} \times 100=\dfrac{3}{100} \times 100$

$\dfrac{x}{100} \times 5=3$

$x=\dfrac{3}{5} \times 100$

x=60

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Question 14

A piece of elastic was stretched by $24 \%$ to a length of $31 \mathrm{~cm}$. Find its unstretched original length.

(a) $24 \mathrm{~cm}$

(b) $26 \mathrm{~cm}$

(c) $25 \mathrm{~cm}$

(d) $20 \mathrm{~cm}$

Sol :

Let the original length be x

According to question,

x+24% of x=31

$x+\dfrac{24}{100} \times x=31$

$\dfrac{100x+24x}{100}=31$

$\dfrac{124x}{100}=31$

$x=\dfrac{31}{124}\times 100$

x=25

High Order Thinking Skills (HOTS)

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Question 15

The sum of two numbers is $\dfrac{28}{25}$ of the first number. The second number is what percent of the first?

Sol :

Let , First number be x

Then , Second number=y

$x+y=\dfrac{28}{25}$of x

$y=\dfrac{28x}{25}-x$

$y=\dfrac{28x-25x}{25}$

$y=\dfrac{3x}{25}$

$\dfrac{y}{x}=\dfrac{3}{25}$

$\dfrac{y}{x}=\dfrac{3}{25} \times 100$

$\dfrac{y}{x}=12%$

y=12% of x

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 8 Percentage and Its Applications Exercise 8H

Exercise 8H

Question

Find the missing value.

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(1) I if P = Rs. 800, R = 5% p.a., T = 2 years.

Sol :

$I=\frac{\text{PRT}}{100}$

$=\frac{800 \times 5 \times 2}{100}$

=80

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(2) I if P = Rs. 5000, R = 6.5% p.a. T = 3 years.

Sol :

$I=\frac{\text{PRT}}{100}$

$=\frac{5000 \times 65\times 3}{100}$

=975

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(3) R is I = Rs. 364 P = Rs. 1300, T = 7 years.

Sol :

$I=\frac{\text{PRT}}{100}$ or $=R\frac{100I}{PT}$

$=\frac{100 \times 364}{1300 \times 7}$

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(4) P if I = Rs. 440, R = 5%, T = 4 years

Sol :

$I=\frac{\text{PRT}}{100}$ or $P=\frac{100I}{RT}$

$=\frac{100 \times 440}{5 \times 4}$

=2200

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(5) T if I = Rs. 455, R = 7%, P = Rs. 1300

Sol :

$I=\frac{\text{PRT}}{100}$ or $T=\frac{100I}{PR}$

$=\frac{100 \times 455}{1300 \times 7}$

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(6) After 2 years, the credit balance in a saving account earning simple interest was Rs. 585.75. The original amount was Rs. 550. What was the interest rate?

Sol :

Simple Interest(585.75-550)=35.75

Interest Rate (R)$=\frac{100I}{PT}$

$=\frac{100 \times 35}{550 \times 2}$

=3.25

Ans : Interest Rate was 3.25%

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(7) In what time will Rs. 1860 amount to Rs. 2641.20 at simple interest of 12% per annum.

Sol :

SI=2641.20-1860=781-20

$I=\frac{PRT}{100}$

or $T=\frac{100I}{PR}$

$=\frac{100\times 781.20}{1860\times 12 \times 100}$

=3.5

Ans : 3.5 years

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(8) Find the simple interest on Rs. 7300 from 10 May 2017 to 10 September 2017 at 5% per annum.

Sol :

$I=\frac{PRT}{100}$

$=\frac{7300 \times 5\times \frac{123}{365}}{100}$

=123

Ans : 123

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(9) A sum of Rs. 400 amounts to Rs. 480 in 4 years. What will it amount ti, if the rate of interest is increased by 2%?

Sol :

I=480-400=80

$I=\frac{PRT}{100}$
or $R=\frac{100I}{PT}$
$=\frac{100 \times 80}{400 \times 4}$
=5

If rate if interest increased 2% per annum,

New (R1)=(5+2)=7%

Then, $I_{1}=\frac{P_{1}R_{1}T_{1}}{100}$
$=\frac{400 \times 4 \times 7}{100}=112$

Therefore, New amount=(P+1)

=400+112=512

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(10) On a certain sum, the simple interest at the end of 6-1/4 years becomes 3/8 of the sum. Find the rate of interest.

Sol :

$I=\frac{PRT}{100}$

$\frac{3}{8}p=\frac{PR\left(\frac{25}{4}\right)}{100}$

$\frac{3}{8}=\frac{R}{16}$

$R=\frac{16\times 3}{8}=6$

Ans : Rate of interest is 6%

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(11) A sum doubles itself in 8 years at simple interest. Find the rate of interest per annum.

Sol :

Let , the sum of money be x

After 8 years amount becomes =2x

S.I=2x-x=x

∴Rate per annum$=\frac{S.I \times 100}{P\times T}$
$=\frac{x\times 100}{x\times 8}=\frac{100}{8}$
=25.5

Ans : Rate of interest is 12.5%

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(12) In how many years will the simple interest on a sum of money be equal to the principal at the rate of 16-2/3% per annum?

Sol :
Let, Principle is P and Interest is also P then $P=\frac{PRT}{100}$
$1=\frac{50 \times T}{3\times 100}$
$T=\frac{100\times 3}{50}$
=6

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 8 Percentage and Its Applications Exercise 8G

Exercise 8G

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Question 1

Find the profit or loss per cent.

(a) C.P. = Rs. 500, S.P. = Rs. 650

Sol :

Profit=(650-500)=150

∴Profit %$=\left(\frac{150}{500}\times 100\right)$=30%

(b) C.P. = Rs. 900, S.P = Rs. 828

Sol :

Loss=900-828=72

∴Loss %$=\left(\frac{72}{900}\times 100\right)$=8%

(c) C.P. = Rs. 325, overheads = Rs. 25, S.P = Rs. 490

Sol :

Total CP=325+25=350

∴Profit %$=\left(\frac{490-350}{350}\times 100\right)$%

$=\left(\frac{140}{350}\times 100\right)$=40%

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Question 2

Find the S.P. of an article if its

(a) C.P. = Rs. 80, profit = 15%

Sol :

Profit$=80 \times \frac{15}{100}$=12

∴SP=80+12=92

(b) C.P = Rs. 950, loss = 8%

Sol :

Loss$=950\times \frac{8}{100}$=76%

SP=950-76=874

(c) C.P = Rs. 190.50, octroi = Rs. 20.50, transportation charges = Rs. 59, loss = 20%

Sol :

Total CP=190.50+20.50+59=270

∴SP$=\frac{100-20}{100}\times 270$

$=\frac{80}{100}\times 270$

=216

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Question 3

Find the C.P. if

(a) S.P. = Rs. 2380, profit = 19%

Sol :

CP$=\left(\frac{100}{100+\text{gain %}}\times \text{SP}\right)$

$=\frac{100}{100+19}\times 2380$

$=\frac{100}{119}\times 2380$

=2000

(b) S.P. = Rs. 510, loss = 15%

Sol :

CP$=\left(\frac{100}{100+\text{gain %}}\times \text{SP}\right)$

$=\left(\frac{100}{100-15}\times 510\right)$

$=\frac{100}{85} \times 510$

=600

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Question 4

A person buys a book for Rs. 200 and sells it for Rs. 225. What will be his gain per cent?

Sol :

Gain%$=\left(\frac{225-200}{200}\times 100\right)$%

$=\frac{25}{200}\times 100$%

=12.5%

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Question 5

A calculator is bought for Rs. 350 and sold at a gain of 15%. What is the selling price of calculator?

Sol :

∴S.P$=\frac{100+15}{100}\times 350$

$=\frac{115}{10}\times 35$

=402.50

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Question 6

By selling a cellphone for Rs. 2400 a shopkeeper makes a profit of 25%. What would be his profit percentage if he sells it for Rs. 2040?

Sol :

C.P$=\frac{100}{100+25}\times 2400$

$=\frac{100}{125}\times 2400$

=1920

Profit %$=\left(\frac{2040-1920}{1920}\times 100\right)$%

$=\left(\frac{120}{1920}\times 100\right)$%

=6.25%

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Question 7

The owner of a cell phone charges his customer 23% more than the cost price. Find the cost price, if a customer paid Rs. 7011 for his cellphone.

Sol :

C.P$=\frac{100}{100+23}\times 7011$

$=\frac{100}{123}\times 7011$

=5700

Cost price of the phone 5700

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Question 8

By selling an article for Rs. 100, a man gains Rs. 15. Find his gain %.

Sol :

C.P=100-15=85

Gain %$=\left(\frac{15}{85}\times 100\right)$%

=17.65%

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Question 9

A trader sells an article and loses 12 and 1/2%. Find the ratio of cost price of the selling price.

Sol :

Let, the CP of an article be 100

∴SP of an article $=\left(100-12\frac{1}{2}\right)$

=100-12.5=87.5

Ratio of CP and SP= 100 : 87.5

=8 : 7

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Question 10

A person purchased 10 dozen pens at the rate of Rs. 40 per dozen. On checking, he found that 20 pens were not working. In order to earn 25% profit, at what price should he sell each pen?

Sol :

10 dozen pens =10×12=120

Rate of per pen $=\frac{40}{12}$

Out of 120 pen 20 pens not working 100 pens working

Price of 100 pens$=\frac{20}{6}\times 100$

=333.3

≃334

25% profit on 334$=\frac{25}{100}\times 334$

=83.5

≃84

25% Profit on 100 pens =(334+84)=418

25% profit on each pen$=\frac{418}{100}$

=4.18

≃5

Ans : He should sell each pen at 5 Rs

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Question 11

When a plot is sold for Rs. 18,700, owner loses 15%. At what price must the plot be sold in order to gain 15%?

Sol :

CP of plot$=\frac{100}{100-15}\times 18700$

$=\frac{100}{85} \times 18700$

=22000

To gain 15% , SP of plot$=\frac{100+15}{100}\times 22000$

=115×220=25300

SP of the plot is 25300

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Question 12

By selling a small plot for Rs. 80,000, I gain 25 per cent. What per cent will i lose if i sell it for Rs. 56,000?

Sol :

CP$=\frac{100}{100+25}\times 80000$

$=\frac{100}{125} \times 80000$

=64000

∴Lose percentage$=\left(\frac{64000-56000}{64000}\times 100\right)$%

$=\left(\frac{8000}{64000}\times 100\right)$%

=12.5 %

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Question 13

A man purchased a car for Rs. 1,35,000 and spent Rs. 25,000 on repairs. At what price was the car sold, if he suffered 10% loss on it?

Sol :

Total CP=135000+25000

=160000

Loss=10%

∴Then profit$=160000 \times \frac{10}{100}$

=16000

∴Total SP=160000-16000=144000

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Question 14

Sudhir earned a profit of 20% by selling 60 apples at the rateof Rs. 42.50 for 5 apples. Find the total cost at which the apples were bought.

Sol :

Rate of 60 apples$=4250 \times \frac{60}{5}$

=2510

∴CP of apples$=\left(\frac{100}{100+20}\times 510\right)$

$=\left(\frac{100}{120}\times 510\right)$

=425

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Question 15

The cost price of 16 pens is equal to the selling price of 12 pens. Find the gain or loss percent?

Sol :

$\frac{SP}{CP}=\frac{16}{12}=\frac{4}{3}$

Loss %$=\frac{4-3}{3}\times 100=\frac{1}{3}\times 100=33\frac{1}{3}$

Ans : Loss$=33\frac{1}{3}$%

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Question 16

If the selling price of 4 articles is equal to the cost price of 5 articles. Find the profit percent?

Sol :

5CP=4SP

$\frac{CP}{SP}=\frac{4}{5}$

∴Profit%$=\frac{5-4}{4}\times 100$

$=\frac{1}{4}\times 100$

=25

Ans : Profit =25%

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Question 17

A fruit seller buys 700 oranges at the rate of Rs. 500 for 100 oranges and another variety of 500 oranges at the rate of Rs. 700 for 100 oranges and sells them at Rs. 84 per dozen. Find the profit per cent.

Sol :

CP of 700 oranges$=\left(\frac{500\times 700}{100}\right)$

=3500

CP of 500 oranges of another variety$=\left(\frac{700}{100}\times 500 \right)$

=3500

∴Total CP=3500+3500=7000

Total number of oranges purchased=700+500=1200

∴Total SP$=\left(\frac{84}{12}\times 1200\right)$

=8400

∴Profit%$=\left(\frac{8400-7000}{7000}\times 100\right)$%

$=\left(\frac{14000}{7000}\times 100\right)$%

=20%

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Question 18

Some articles were bought at 6 for Rs. 5 and sold at 5 for Rs. 6. Find the gain per cent.

Sol :

Let, Number of articles bought =30

∴CP of 30 articles $=\left(\frac{5}{6}\times 30\right)$

=25

∴SP of 30 articles$=\left(\frac{6}{5}\times 30\right)$

=36

∴Gain%$=\left(\frac{36-25}{25}\times 100\right)$%

$=\left(\frac{11}{25} \times 100\right)$%=44%

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Question 19

An article is sold at a gain of 15%. Had it been sold for Rs. 27 more, the profit would have been 20%. Find the cost price of the article.

Sol :

100 units CP

15% gain SP₁=115

20% gain SP₂=120

So, 5 unit =27

1 unit $=\frac{27}{5}$

∴100$=\frac{27}{5}\times 100$=540

CP of the article 540

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Question 20

A dealer sold two types of goods for Rs. 10,000 each. On one of them, he lost 20% and on the other, he gained 20%. Find his gain or loss per cent on the entire transaction.

Sol :

Total SP=10000+10000=20000

Since, we know that

CP on loss$=SP \times \frac{100}{100-20}$

CP on profit$=SP\times \frac{100}{100+20}$

∴Total CP$=\left[10000\times \frac{100}{100-20}\right]+\left[10000\times \frac{100}{100+20}\right]$

$=\left(10000\times \frac{100}{80}\right)+\left(10000 \times \frac{100}{120}\right)$

$=50000\times \left(\frac{1}{4}+\frac{1}{6}\right)$

$=50000\times \frac{3+2}{12}=\frac{62500}{3}$

∴Loss$=\frac{62500}{3}-20000$

$=\frac{62500-60000}{3}=\frac{2500}{3}$

∴Loss %$=\left(\dfrac{\frac{250000}{3}}{\frac{62500}{3}} \times 100\right)$%

$=\left(\frac{2500}{62500}\times 100\right)$=4%

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 8 Percentage and Its Applications Exercise 8F

Exercise 8F

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Question 1

55 per cent of the students in a school are girls. What percentage of the students are boys? Find the number of students, if there are 216 boys.

Sol :

∴Percentage of boys=100-55=45%

45% of student=216

1% of student$=\frac{216}{45}$

45% of student$=\frac{216 \times 100}{45}$=480

∴Total number of student=480

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Question 2

If 10% is deducted from a bill, Rs. 7200 remains to be paid. How much is the bill?

Sol :

∴Remaining bill=(100-10)=90%

90% bill=7200

1% bill $=\frac{7200}{90}$

100% bill $=\frac{7200 \times 100}{90}$=8000

∴Total bill=8000

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Question 3

Calculation gives the length of a line segment as 6.4 cm, while from drawing and measurement it is obtained as 6.6 cm. Find the error per cent.

Sol :

∴Error length=(6.6-6.4)=0.2 cm

In 6.4 cm the error is 0.2 cm

In 1 cm the error is $=\frac{0.2}{6.4}$ cm

In 100 cm the error is $=\frac{0.2\times 100}{6.4}=\frac{25}{8}=3\frac{1}{8}$ cm

∴Error Percentage is $3\frac{1}{8}$%

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Question 4

Atul deposited 30% of his income in a bank. After spending 50% of the remaining, he had Rs. 10,500 left with him. What is his income?

Sol :

Remaining income after depositing in bank=100-30=70%

50% of 70%=35%

35% of income is 10500

1% of income is $\frac{10500}{35}$

100% of income is $=\frac{10500 \times 100}{35}$=30000

∴Atul's income is 30000

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Question 5

Manish obtained 498 marks out of 600 marks and Aravind scored 640 marks out of 800 marks. Whose performance is better?

Sol :

∴Percentage of Manish score$=\left(\frac{498}{600} \times 100\right)$=83 %

∴Percentage of Arvind's score$=\left(\frac{640}{800}\times 100\right)$=80%

Ans : Manish's performance is better than Arvind performance

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Question 6

In a graduate class of 200, 40% are women and 1/5 becomes lecturers. If the number of men who became lecturers is twice that of women, calculate approximate percentage of men who became lecturers.

Sol :

Number of women$=\frac{40}{100}\times 200$=80

Number of women who become lecturer$=80\times \frac{1}{5}$=16

Number of men who becomes lecturer=16×2=32

Number of men=200-80=120

∴Percentage of men who becomes lecturer$=\left(\frac{32}{120}\times 100\right)$

=26.6%

≃27%

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Question 7

The price of an article is reduced by 25%. In order to retain the original price, by what percentage should the present price be increased?

Sol :

Let the price 100

25% reduced new price 75

So the price raised should be $=\left(\frac{25}{75}\times 100\right)$=33.33%

Ans : The present price increased 33.33%

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Question 8

In a mixture of milk and water, the proportion of water by weight is 75%. If in the 60 g mixture, 15 g of water is added, what would be the percentage of water?

Sol :

In 60 g mixture , weight of water$=\left(\frac{75}{100}\times 60\right)$=45 gm

15 g water is added , now weight of water=45+15=60gm

Now , Percentage of water $=\left(\frac{60}{75}\times 100\right)$=80%

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Question 9

One litre of water is evaporated from a 6 litre solution containing 4% sugar. Find the percentage of sugar in the remaining solution.

Sol :

Quality of sugar in 6 litre solution $=\left(\frac{4}{100}\times 6\right)$=0.24 litre

1 litre of water evaporated from a 6 litre solution

Now, quantity of solution=(6-1)=5 litres

Percentage of sugar in remaining solution$=\left(\frac{0.25}{5}\times 100\right)$=4.8%

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Question 10

State Electricity Board gives 15% discount on electricity bills, if it is paid before due date. A person gets Rs. 54 as discount. What was the actual amount of the bill?

Sol :

State Electricity Board gives 15 Rs discount on 100

State Electricity Board gives 1 Rs discount on $=\frac{100}{15}$

State Electricity Board gives 54 Rs discount on $=\frac{100\times 54}{15}$=360

Ans : Actual deposit of bill is 360

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 8 Percentage and Its Applications Exercise 8E

Exercise 8E

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Question 1

Ravi’s class has 18 boys and 12 girls. What is its percentage composition?

Sol :
∴Percentage of boys$=\frac{18}{30}\times 100$=60%

∴Percentage of girls$=\frac{12}{30}\times 100$=40%

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Question 2

Chalk contains 10% calcium, 3% carbon and 12% oxygen. Find the amount of carbon and calcium (in grams) in 2 and $\frac{1}{2}$ kg of chalk.

Sol :

Amount of carbon$=\left(2\frac{1}{2}\times \frac{3}{100}\right)$ kg

$=\frac{6}{2}\times \frac{3}{100}=\frac{3}{40}$

∴Amount of calcium$=\left(2\frac{1}{2}\times \frac{10}{100}\right)$ kg

$=\left(\frac{5}{2} \times \frac{18}{100}\right)=\frac{1}{4}$

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Question 3

An alloy contains 4% tin, 1% zinc and the remaining copper.

(a) What is the percentage composition of the alloy?

Sol :

Percentage of tin=4%

Percentage of zinc=1%

Percentage of copper=(100-5)=95%

(b) Find the mass (in kg) of each metal in 5 tonnes of the alloy.

Sol :

5 tonnes=5000 kg

Mass of tin $=\left(5000 \times \frac{4}{100}\right)$=200 kg

Mass of zinc $=\left(5000 \times \frac{1}{100}\right)$=50 kg

Mass of copper $=\left(5000 \times \frac{95}{100}\right)$=4750 kg

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Question 4

A packet of cake mix has the composition of its contents shown on the label. Calculate the percentage composition of the cake mix.

Nutritional value (per 50 g serve)
Protein	3.5 g
Fat	5.5 g
Carbohydrates	27 g
Other ingredients	14 g

Sol :

∴Percentage of protein$=\frac{3.5}{50} \times 100$=7%

∴Percentage of fat$=\frac{5.5}{50} \times 100$=11%

∴Percentage of carbohydrates$=\frac{27}{50} \times 100$=54%

∴Percentage of other ingredients$=\frac{14}{50} \times 100$=28%

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Question 5

The average composition (by weight) of milk is shown in the table.

Ingredients	Percentage
Carbohydrate	5
Protein	3
Fat	4
Water	87
Other	1

(a) How many grams are there of each component in 1 kg of milk?

Sol :

[1 kg=1000 gm]

∴Quantity of carbohydrates$=\left(1000 \times \frac{5}{100}\right)$=50 gm

∴Quantity of protein$=\left(1000\times \frac{3}{100}\right)$=30gm

∴Quantity of fat$=\left(1000 \times \frac{4}{100}\right)$=40 gm

∴Quantity of water$=\left(1000 \times \frac{87}{100}\right)$=870 gm

∴Quantity of other ingredient$=\left(1000 \times \frac{1}{100}\right)$=10 gm

(b) How many grams of proteins are there in 7.5 kg of milk?

Sol :

7.5 kg=7500 gm

∴Quantity of protein$=\left(7500\times \frac{3}{100}\right)$=225 gm

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 8 Percentage and Its Applications Exercise 8D

Exercise 8D

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Question 1

Increase:

(a) Rs. 50 by 20%

Sol :

$=\frac{20}{100}\times 50$

=10

∴New increased amount=50+10=60

(b) Rs. 700 by 8%

Sol :

$=\frac{8}{100}\times 700$

=56

∴New increased amount=700+56=756

(c) 600 g by 18%

Sol :

$=\frac{18}{100}\times 600$

=108

∴New increased amount=600+108=708g

(d) 4L by 15%

Sol :

$=\frac{15}{100}\times 4$

=0.6

∴New increased weight=(4+0.6)L=4.6 L

(e) 8 km by 19%

Sol :

$=\frac{19}{100}\times 8$

=1.52

∴New increased distance=(8+1.52)=9.52 km

(f) 5 kg by 23%

Sol :

$=\frac{23}{100}\times 5$

=1.15

∴New increased weight=(5+1.15)=6.15 kg

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Question 2

Decrease:

(a) Rs. 170 by 10%

Sol :

$=\frac{10}{100}\times 170$

=17

∴New decreased amount=(170+17)=153

(b) Rs. 2500 by 18%

Sol :

$=\frac{18}{100}\times 2500$

=450

∴New decreased amount=(2500-450)=2050

(c) 1 ha by 28%

Sol :

$=\frac{28}{100}\times 1$

=0.28

∴New decreased amount=(1-0.28)=0.72 ha

(d) 12 tonnes by $24\frac{2}{3}$% tonnes

Sol :

$=24\frac{2}{3}\% \text{ of } 12$

$=\frac{74}{300}\times 12$=2.96

∴New decreased weight=(12-2.96)=9.04

(e) 24 m by 22%

Sol :

$=\frac{22}{100}\times 24$

=5.28

∴New decreased unit=(24-5.28)=18.72 m

(f) 480 g by 20%

Sol :

$\frac{20}{100}\times 480$

=96

∴New decreased weight=480-96=384 g

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Question 3

The entrance fee at a science museum is Rs. 50. Senior citizens recieve a 20% discount. How much fee does a senior citizen pay?

Sol :

Discount for senior citizen$=2\left(50\times \frac{20}{100}\right)$=10

∴Fees for senior citizen=50-10=40

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Question 4

What is the final price of a Rs. 4500 leather jacket that is on sale for 40% off?

Sol :

Discount price$=\left(\frac{40}{100}\times 4500\right)$

=1800

∴Final price of leather jacket=4500-1800=2700

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Question 5

Increase Rs. 2000 by 10% and then decrease the new amount by 10%.

Sol :

∴Price increases$=\left(\frac{10}{100}\times 2000\right)$=200

∴New increased amount=(2000+200)=2200

New price decreases$=\left(\frac{2110}{100}\times 2200\right)$=220

∴New decreased amount=2200-220=1980

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Question 6

Decrease Rs. 500 by 15% and then increase the result by 15%.

Sol :

∴Price decreases$=\left(\frac{15}{100}\times 500\right)$=75

∴Decreased price=500-75=425

New increased price$=\left(\frac{15}{100}\times 425\right)$=63.75

∴New increased price=425+63.75=488.75

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Question 7

Find the per cent increase for the following.

(a) original price = Rs. 800, new price = Rs. 872

Sol :

Increased price=872-800=72

∴Percentage of new price$=\left(\frac{72}{800}\times 100\right)$=9%

(b) old income = Rs. 1,20,000, new income = Rs. 1,50,000

Sol :

∴Increased income=150000-120000=30000

∴Percentage of new income$=\left(\frac{30000}{120000}\times 100\right)$=25%

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Question 8

Find the percent decrease for the following.

(a) From 500 to 100

Sol :

500-100=400

∴Decreased percentage$=\left(\frac{400}{500}\times 100\right)$=80%

(b) Original price = Rs. 300, new price = Rs. 270

Sol :

Decreased price=300-270=30

∴Decreased percentage$=\left(\frac{30}{300}\times 100\right)$=10%

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Question 9

A property which was valued at Rs. 40,000 five years ago is now valued at Rs. 60,000. What is the percentage increase in value?

Sol :

Decreased value=60000-40000=20000

∴Percentage of increased value$=\left(\frac{20000}{40000}\times 100\right)$=50%

Exercise 8 E

Question 1

Exercise 8 D

Question 1

Exercise 8 C

Question 1

Exercise 8 B

Question 1

Exercise 8 A

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Exercise 8H

Question

Exercise 8G

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Exercise 8F

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Exercise 8E

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 8D

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

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