Class 8 RD Sharma Solutions – Chapter 12 Percentage – Exercise 12.2 | Set 1

Question 1. Find:
(i) 22% of 120
(ii) 25% of Rs 1000
(iii) 25% of 10 kg
(iv) 16.5% of 5000 meter
(v) 135% of 80 cm
(vi) 2.5% of 10000 ml

Solution:

(i) 22% of 120

22% of 120 can be termed as (22/100) X 120 = 26.4

(ii) 25% of Rs 1000

25% of Rs 1000 can be termed as (25/100) X 1000 = Rs 250

(iii) 25% of 10 kg

25% of 10 kg can be termed as (25/100) X 10 = 2.5 kg

(iv) 16.5% of 5000 meter

16.5% of 5000 meter can be termed as (16.5/100) X 5000 = 825 meter

(v) 135% of 80 cm

135% of 80 cm can be termed as (135/100) X 80 = 108 cm

(vi) 2.5% of 10000 ml

2.5% of 10000 ml can be termed as (2.5/100) X 10000 = 250 ml

Question 2. Find the number ‘a’, if
(i) 8.4% of a is 42
(ii) 0.5% of a is 3
(iii) 1/2 % of a is 50
(iv) 100% of a is 100

Solution:

(i) Given, 8.4% of a is 42

So, (8.4/100) × a = 42

a = 4200/8.4 = 500

Hence, a = 500

(ii) Given, 0.5% of a is 3

So, (0.5/100) × a = 3

a = 300/0.5 = 600

Hence, a = 600

(iii) Given, 1/2 % of a is 50

So, (0.5/100) × a = 50

a = 5000/0.5 = 10000

Hence, a = 10000

(iv) Given, 100% of a is 100

So, (100/100) × a = 100

a = 100

Hence, a = 100

Question 3. x is 5% of y, y is 24% of z. If x = 480, find the values of y and z.

Solution:

Given, x is 5% of y

y is 24% of z

x = 480

Since, x = 5% of y

We can write, 480 = 5% of y

So, 480 = (5/100) × y

y = 9600

Also, y = 24% of z

So, 9600 = (24/100) × z

z = 40000

Hence, y is 9600 and z is 40000

Question 4. A coolie deposits Rs. 150 per month in his post office Saving Bank account. If this is 15% of his monthly income, find his monthly income.

Solution:

Let a be the monthly income of coolie

Given, a coolie deposits Rs. 150 per month in his post and this is equal to 15% of his monthly income

So, 15 % of a = Rs 150

(15/100) × a = 150

a = Rs 1000

Hence, the monthly income of coolie is Rs 1000 

Question 5. Asha got 86.875% marks in the annual examination. If she got 695 marks, find the number of marks of the Examination.

Solution:

Let a be the total number of marks in the Exam 

Given, marks scored by Asha is 695 and this is 86.875% marks

So, 86.875% of a = 695

(86.875/100) × a = 695

a = 800 marks

Hence, the examination is of 800 marks

Question 6. Deepti went to school for 216 days in a full year. If her attendance is 90%, find the number of days on which the school was opened?

Solution:

Given, Number of days Deepti went to school is 216 and this is 90 % of her attendance

Let a be the total number of days, the school was opened.

So, 90 % of a = 216

(90/100) × a = 216

a = 240 days

Hence, the school was opened for 240 days

Question 7. A garden has 2000 trees. 12% of these are mango trees, 18% lemon and the rest are orange trees. Find the number of orange trees.

Solution:

Given, the total number of trees = 2000

12% of these are mango trees, 18% lemon and the rest are orange trees

So, 12 % of 2000 are mango trees

12 % of 2000 = Number of Mango trees 

Number of Mango trees = (12/100) × 2000 = 240 trees

Number of Lemon trees = 18 % of 2000 = (18/100) × 2000 = 360 trees

And, the number of Orange trees = Total number of trees — (Number of Mango trees+ Number of Lemon trees)

= 2000 – (240 + 360) = 1400

Hence, there are 1400 orange trees in the garden

Question 8. Balanced diet should contain 12% of protein, 25% of fats, and 63% of carbohydrates. If a child needs 2600 calories in this food daily, find in calories the amount of each of these in his daily food intake.

Solution:

Given, total amount of calories needed = 2600

So, the amount of Protein needed = 12 % of 2600

= (12/100) × 2600 = 312 calories

The amount of Fats needed = 25 % of 2600

= (25/100) × 2600 = 650 calories

The amount of Carbohydrate needed = 63 % of 2600

= (63/100) × 2600 = 1638 calories 

Hence, the amount of calories needed in Protein, Fats and Carbohydrate is 312, 650 and 1638 calories respectively

Question 9. A cricketer scored a total of 62 runs in 96 balls. He hits 3 sixes, 8 fours, 2 twos and 8 singles. What percentage of the total runs came in :
(i) Sixes
(ii) Fours
(iii) Twos
(iv) Singles

Solution:

Given, a cricketer scored a total of 62 runs in 96 balls

i) The total runs scored in form of Sixes = 3 × 6 = 18

So, percentage of runs scored in form of Sixes = (18/62) × 100 = 29.03%

ii) The total runs scored in form of Fours = 8 × 4 = 32

So, percentage of runs scored in form of Fours = (32/62) × 100 = 51.61%

iii) The total runs scored in form of Twos = 2 × 2 = 4

So, percentage of runs scored in form of Twos = (4/62) × 100 = 6.45%

iv) The total runs scored in form of Singles = 1 × 8 = 8

So, percentage of runs scored in form of Singles = (8/62) × 100 = 12.9%

Question 10. A cricketer hits 120 runs in 150 balls during a test match. 20% of the runs came in 6’s, 30% in 4’s, 25% in 2’s and the rest in 1’s. How many runs did he score in :
(i) 6’s
(ii) 4’s
(iii) 2’s
(iv) singles
What % of his shots were scoring ones?

Solution:

Given, a cricketer hits 120 runs in 150 balls

i) Number of runs scored in form of 6’s = 20 % of 120

= (20/100) × 120 = 24 runs

ii) Number of runs scored in form of 4’s = 30 % of 120

= (30/100) × 120 = 36 runs

iii) Number of runs scored in form of 2’s = 25 % of 120

= (25/100) × 120 = 30 runs

iv) Number of runs scored in form of singles = 120 – (24 + 36 + 30) = 30 runs

Now, the percentage of runs scored in singles = (30/100) × 120 = 25%

Hence, 25 % of runs scored in form of singles

Question 11. Radha earns 22% of her investment. If she earns Rs. 187, then how much did she invest?

Solution:

Given, the amount of money Radha earned through investment = Rs 187

Let a be the amount of money she invested

So, we can say that 22 % of a = 187

(22/100) × a = 187

a = Rs 850

Hence, Radha invested Rs 850  

Question 12. Rohit deposits 12% his income in a bank. He deposited Rs. 1440 in the bank during 1997. What was his total income for the year 1997?

Solution:

Given, Rohit deposits 12% of his income in a bank. 

Let a be the total income of Rohit in year 1997

So, we can say 12 % of a = 1440

(12/100) × a = 1440

a = Rs 12000

Hence, the total income of Rohit in year 1997 is Rs 12000

Question 13. Gunpowder contains 75% nitre and 10% sulphur. Find the amount of the gunpowder which carries 9 kg nitre. What amount of gunpowder would contain 2.3 kg sulphur?

Solution:

Given, Gunpowder contains 75% nitre and 10% sulphur

Let a be the total amount of gunpowder

i) So, we can say 75 % of a = 9 kg Nitre

(75/100) × a = 9

a = 12 kg

Hence, 12 kg gunpowder carries 9 kg nitre

ii) So, we can say 10 % of a = 2.3 kg Sulphur

(10/100) × a = 2.3

a = 23 kg

Hence, 23 kg gunpowder carries 2.3 kg sulphur

Chapter 12 Percentage – Exercise 12.2 | Set 2