__ Percentage __

__EXERCISE 11(A)__

__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)__

__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%

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%).

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%

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

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

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?**

Answer: 12% of the earlier soldiers.

**(i) his monthly expenditure as percent.**

**(ii) his monthly savings as percent.**

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

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

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

₹ 26,880 is the new monthly income.

**(i) the reduction in the price of the article**

**(ii) the reduced price of the article.**

(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

(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)__

__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.**

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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