Concise Mathematics, Middle School, Class 6 ICSE, Ch-11, Percentage

 Percentage 

EXERCISE 11(A)

1. Express each of the following statements in percentage form:

(i) 13 out of 20

Solution: (13/20) x 100 % = 65%

(ii) 21 eggs out of 30 are good

Solution: (21/30) x 100 = 70%

2. Express the following fractions as percent:

(i) 3/200

Solution: (3/200) x 100 %= 1.5%

(ii) 6/5

Solution: (6/5) x 100 %= 120%

(iii) 65/80

Solution: (65/80) x 100 %= 81.25%

(iv) 2/3

Solution: (2/3) x 100 %= 66 .67 %

3. Express as percent:

(i) 0.10

Solution: 0.10 x 100% = 10%

Answer: 10%

(ii) 0.02

Solution: 0.02 x 100 = 2%

(iii) 0.7

Solution: 0.7 x 100 = 70%

(iv) 0.15

Solution: 0.15 x 100 = 15%

Answer: 15%

(v) 0.032

Solution: 0.032 x 100 = 3.2%

 

4. Convert the following into fractions in their lowest terms:

(i) 8%

Solution: 8/100 = 4/50 = 2/25

(ii) 20%

Solution: 20/100 = 1/5

(iii) 85%

Solution: 85/100 = 17/20

(iv) 250%

Solution: 250/100 = 5/2

(v) 122%

Solution: 122/100 = 61/50

5. Express as decimal fractions:

(i) 25%

Solution: 25/100 = 0.25

(ii) 108%

Solution: 108/100 = 1.08

(iii) 95%

Solution: 95/100 = 0.95

(iv) 4.5%

Solution: 4.5/100 = 0.045

(v) 29.2%

Solution: 29.2/100 = 0.292

6. Express each of the following numbers as percent:

(i) 7

Solution: 7x100% =  = 700%

(ii) 2

Solution: 2x 100% =  = 200%

(iii) 19.5

Solution: 19.5x100% = = 1950%

(iv) 5.37

Solution: 5.37 x 100% = 537%

 

EXERCISE 11(B)

Express:

(i) 5 as a percentage of 25

Solution: (5/25) x 100 %= 20%

ii)80 paise as a percent of Rs 4

(80/400)x 100%= 20%

(iii) 700 g as a percentage of 2.8 kg

Solution: First, converting 2.8 kg to grams: 2.8 kg = 2800 g

Then,  the percentage: (700/2800) x 100% = 25%

 2 Express the first quantity as a percent of the second:

(i) 40 p, ₹ 2

Solution: (40/200) x 100% = 20%

(ii) 500 g, 6 kg

Solution: First, converting 6 kg to grams: 6 kg = 6000 g

Then, find the percentage: (500/6000) x 100% = 8.33%

 (iv) 90 cm as a percent of 4.5 m

Solution: First, converting 4.5 m to centimeters: 4.5 m = 450 cm

Then, find the percentage: (90/450) x 100 %= 20%

(iii) 42 seconds, 6 minutes

Solution: First, converting 6 minutes to seconds: 6 minutes = 360 seconds

Then, the percentage: (42/360) x 100 = 11.67%

Answer: 11.67%

3. Find the value of each of the following:

(ii) 90% of 130

Solution: 90% of 130 = 117 (90/100 x 130)

(i) 20% of ₹150

Solution: 20% of ₹150 = ₹30 (20/100 x ₹150)

(iv) 7.5% of 500 kg

Solution: 7.5% of 500 kg = 37.5 kg (7.5/100 x 500)

(iii) 15% of 2 minutes

Solution: 15% of 2 minutes = 18 seconds (15/100 x 120)

4. If a man spends 70% of his income, what percent does he save?

Solution: He saves 30% (100% - 70% = 30%).

 5. A girl gets 65 marks out of 80. What percentage of marks does she get?

Solution: 65/80 x 100%

She gets 81.25%

6. A class contains 25 children, of which 6 are girls. What is the percentage of boys in the class?

Solution: 19/25 x 100%

The percentage of boys is 76%

 7. A tin contains 20 liters of petrol. Due to leakage, 3 liters of petrol is lost. What is the percentage of petrol left?

Solution: 17/20 x 100%

The percentage of petrol left is 85%

8. An alloy contains 45% copper and the rest is zinc. Find the weight of zinc in 20 kg of the alloy.

Solution: percentage of zinc=55%

55% of 20kg

 The weight of zinc is 11 kg

 11. In a plot of ground of area 6000 sq.m, only 4500 sq.m is construction. What percentage of area is to be left without construction?

 Solution: (6000 - 4500) / 6000 = (1500 / 6000 )x 100% = 25%

25% of the area is to be left without construction.

 9.A boy got 60 out of 80 in Hindi, 75 out of 100 in English, and 65 out of 70 in Arithmetic. In which subject is his percentage of marks the best? Also, find his overall percentage.

Solution:

Hindi: (60/80) x 100 = 75%

English: (75/100) x 100 = 75%

Arithmetic: (65/70) x 100 = 92.86%

Answer: His percentage of marks is best in Arithmetic.

Overall percentage: (60 + 75 + 65) / (80 + 100 + 70) = 200 / 250 = 80%

10. 60 more soldiers joined a camp of 500 soldiers. What percentage of the earlier soldiers?

 Solution: (60 / 500) x 100 = 12%

Answer: 12% of the earlier soldiers.

 12. Mr. Sharma has a monthly salary of ₹ 8,000. If he spends ₹6,400 every month, find:

(i) his monthly expenditure as percent.

(ii) his monthly savings as percent.

 Solution:

(i) (6400 / 8000) x 100 = 80%

(ii) (8000 - 6400) / 8000 = 1600 / 8000 = 20%

Answer: (i) 80% (ii) 20%

 13. The monthly salary of Rohit is ₹ 24,000. If his salary increases by 12%, find his new monthly salary.

 Solution: (24,000 x 12%) + 24,000 = 2880 + 24,000 = 26,880

 ₹ 26,880 is the new monthly income.

 14. In a sale, the price of an article is reduced by 30%. If the original price of the article is ₹ 1,800, find:

(i) the reduction in the price of the article

(ii) the reduced price of the article.

 Solution:

(i)                  Reduction in price=(30% of 1800) =  ₹ 540

(ii) Reduced price=1800 - 540 =  ₹ 1,260

15. Evaluate:

(i) 30% of 200 + 20% of 450 - 25% of 600

(ii) 10% of ₹ 450 - 12% of ₹ 500 + 8% of ₹ 500

 Solution:

(i) (30% of 200) + (20% of 450) - (25% of 600) = 60 + 90 - 150 = 0

(ii) (10% of 450) - (12% of 500) + (8% of 500) = 45 - 60 + 40 = 25

 

EXERCISE 11(C)

1. The price of rice rises from ₹30 per kg to ₹36 per kg. Find the percentage rise in the price of rice.

Ans- The difference in price = ₹36 - ₹30 = ₹6

percentage rise in price = (6/30) x 100%= 20%

 The price of rice has risen by 20%.

2. The population of a small locality was 4000 in 1979 and 4500 in 1981. By what percent had the population increased?

 Difference in population = 4500 - 4000 = 500

Percentage increase in population =(500 ÷ 4000 ) x 100% = 12.5%

The population had increased by 12.5%.

3. The price of a scooter was ₹8,000 in 1975. It came down to ₹6,000 in 1980. By what percent had the price of the scooter come down?

Ans- Difference in price = ₹8,000 - ₹6,000 = ₹2,000

Step 2: percentage =( ₹2,000 ÷ ₹8,000 )x 100% = 25%

The price of the scooter had come down by 25%.

4. Find the resulting quantity when

(i) ₹400 is decreased by 8%:

 8% of ₹400 = ₹400 x 0.08 = ₹32

The resulting Quantity =  ₹400 - ₹32 = ₹368

(ii) 25 km is increased by 5%:

 5% of 25 km = 25 x 0.05 = 1.25 km

 resulting quantity= 25 + 1.25 = 26.25 km

(iii) A speed of 600 km/h is increased by 12%:

 12% of 600 km/h = 600 x 0.12 = 72 km/h

Resulting quality  = 600 + 72 = 672 km/h

(iv) There is a 2.5% increase in a salary of ₹62,500:

 2.5% of ₹62,500 = ₹62,500 x 0.025 = ₹1,562.50

Resulting quantity = ₹62,500 + ₹1,562.50 = ₹64,062.50

5. The population of a village decreased by 12%. If the original population was 25,000, find the population after the decrease.

12% of 25,000 = 25,000 x 0.12 = 3,000

Population after the decrease  = 25,000 - 3,000 = 22,000

6. Out of a salary of ₹13,500, I keep one-third as savings. Of the remaining money, I spend 50% on food and 20% on house rent. How much do I spend on food and house rent?

one-third of ₹13,500 = ₹13,500 ÷ 3 = ₹4,500 (savings)

 Subtract ₹4,500 from ₹13,500 = ₹13,500 - ₹4,500 = ₹9,000 (remaining money)

50% of ₹9,000 = ₹9,000 x 0.5 = ₹4,500 (spent on food)

20% of ₹9,000 = ₹9,000 x 0.2 = ₹1,800 (spent on house rent)

7. A tank can hold 50 liters of water. At present, it is only 30% full. How many liters of water should I put into the tank so that it becomes 50% full?

 30% of 50 liters = 50 x 0.3 = 15 liters (current amount)

 Find 50% of 50 liters = 50 x 0.5 = 25 liters (desired amount)

Amount to be added = 25 - 15 = 10 liters .

8. In an election, there are a total of 80,000 voters and two candidates, A and B. 80% of the voters go to the polls, out of which 60% vote for A. How many votes does B get?

 80% of 80,000 = 80,000 x 0.8 = 64,000 (voters who went to the polls)

votes for A

60% of 64,000 = 64,000 x 0.6 = 38,400

votes for B

64,000 - 38,400 = 25,600

9. 70% of our body weight is made up of water. Find the weight of water in the body of a person whose body weight is 56 kg.

weight of water

70% of 56 kg = 56 x 0.7 = 39.2 kg

10. Only one-fifth of the available water is in liquid form. This limited amount of water is replenished and used by man recurrently. Express this information as percent, showing:

(i) Water available in liquid form:

i) 1/5 as a percentage = (1/5) x 100 %= 20%

(ii) Water available in frozen form:

4/5 as a percentage = (4/5) x 100 %= 80%

Answer: 80% of water is available in frozen form.

11. By weight, 90% of tomato and 78% of potato is water. Find:

(i) The weight of water in 25 kg of tomato:

90% of 25 kg = 25 x 0.9 = 22.5 kg

(ii) The total quantity, by weight, of water in 90 kg of potato and 30 kg of tomato:

78% of 90 kg = 90 x 0.78 = 70.2 kg (water in potato)

 90% of 30 kg = 30 x 0.9 = 27 kg (water in tomato)

Add 70.2 kg and 27 kg = 70.2 + 27 = 97.2 kg

Answer: The total quantity of water is 97.2 kg.

12. Find the number that is:

(i) 50% more than 48:

 50% of 48 = 48 x 0.5 = 24

Add 24 to 48 = 48 + 24 = 72

 The number is 72.

(ii) 30% less than 70:

 30% of 70 = 70 x 0.3 = 21

S Subtract 21 from 70 = 70 - 21 = 49

The number is 49.

13. Evaluate:

(i) 8% of 900 - 12% of 750 + 20% of 165:

 8% of 900 = 900 x 0.08 = 72

 12% of 750 = 750 x 0.12 = 90

 20% of 165 = 165 x 0.2 = 33

Number = 72 - 90 +33= -18 + 33 = 15

(ii) 70% of 70 + 90% of 90 - 120% of 120:

S 70% of 70 = 70 x 0.7 = 49

90% of 90 = 90 x 0.9 = 81

120% of 120 = 120 x 1.2 = 144

Add 49 and 81 = 49 + 81 = 130

Subtract 144 from 130 = 130 - 144 = -14

The result is -14.

14. Approximately 97.3% water on the earth is not fit for drinking. Find:

(i) The percentage of water on the earth that is fit for drinking:

 the remaining percentage = 100 - 97.3 = 2.7%

 2.7% of water on earth is fit for drinking.

(ii) The total volume of water available in a certain part of the earth where there is 21,600 m³ of drinking water:

 total volume = 21,600 / 0.027 (convert 2.7% to a decimal) = 800,000 m³

The total volume of water is approximately 800,000 m³.

15. Air is an important inexhaustible natural resource. It is essential for the survival of human beings , microbes , plants and animals. The following table shows the Percentage of various gases in air.

In 800 m³ of air, calculate the approximate quantities of nitrogen, oxygen, and other gases

Answer-

 the quantity of nitrogen = 800 x 0.78 = 624 m³

the quantity of oxygen = 800 x 0.21 = 168 m³

the quantity of other gases = 800 x 0.01 =8 m³

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