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1. NCERT Solutions - Mathematics, Class 6

CHAPTERS

1. Knowing Our Numbers

2. Whole Numbers

3. Playing With Numbers

4. Basic Geometrical Ideas

5. Understanding Elementary Shapes

6. Integers

7. Fractions

8. Decimals

9. Data Handling

10. Mensuration

11. Algebra

12. Ratio and Proportion

13. Symmetry

EXERCISES

1. Exercise 12.1

2. Exercise 12.2

3. Exercise 12.3

Q1) There are 20 girls and 15 boys in a class.

(a) What is the ratio of the number of girls to the number of boys?

(b) What is the ratio of the number of girls to the total number of students in the class?

Q2) Out of 30 students in a class, 6 like football,

12 like cricket and remaining like tennis. Find

the ratio of

(a) Number of students liking football to

the number of students liking tennis.

(b) The number of students liking cricket to total

number of students.

Q3) See the figure and find the ratio of

(i) The number of triangles to the number of circles

inside the rectangle.

(ii) Number of squares to all the figures inside the

rectangle.

(iii) The number of circles to all the figures inside the

Q4) Distances travelled by Hamid and Akhtar in an hour is 9 km and 12 km. Find the

the ratio of the speed of Hamid to the speed of Akhtar.

Q5) Fill in the following blanks:

\frac{15}{18}=\frac{?}{6}=\frac{10}{?}=\frac{?}{30}\left[are\ they\ equivalent\ ratios?\right]

Q6) Find the ratio of the following :

(i) 81 to 108 (ii) 98 to 63

(iii) 33 km to 121 km (iv) 30 minutes to 45 minutes

Q7) Find the ratio of the following:

(a) 30 minutes to 1.5 hours (b) 40 cm to 1.5 m

(c) 55 paise to ` 1 (d) 500 mL to 2 litres

Q8) In a year, Seema earns 1,50,000 and saves 50,000. Find the ratio of

1,50,000 and saves

(a) Money that Seema earns to the money she saves.

(b) Money that she saves to the money she spends.

Q9) There are 102 teachers in a school of 3300 students. Find the ratio of the number

of teachers to the number of students.

Q10)

In a college, out of 4320 students, 2300 are girls. Find the ratio of

(a) Number of girls to the total number of students.

(b) The number of boys to the number of girls.

(c) The number of boys to the total number of students.

Q11) Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining

opted table tennis. If a student can opt only one game, find the ratio of

(a) Number of students who opted basketball to the number of students who opted

table tennis.

(b) The number of students who opted cricket to the number of students opting basketball.

(c) The number of students who opted basketball to the total number of students.

Q12) Cost of a dozen pens is 180 and cost of 8 ball pens are 56. Find the ratio of the cost

of a pen to the cost of a ball pen.

Q13) Consider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the

following table that shows some possible breadths and lengths of the hall.

Q15) Mother wants to divide ` 36 between her daughters Shreya and Bhoomika in the ratio

of their ages. If age of Shreya is 15 years and age of

Bhoomika is 12 years, find how much Shreya and Bhoomika

will get.

Q1) Determine if the following are in proportion.

(a) 15, 45, 40, 120 (b) 33, 121, 9,96 (c) 24, 28, 36, 48

(d) 32, 48, 70, 210 (e) 4, 6, 8, 12 (f) 33, 44, 75, 100

16) Present age of father is 42 years and that of his son is 14

years. Find the ratio of

(a) Present age of father to the present age of son.

(b) Age of the father to the age of son, when son was 12

years old.

(c) Age of father after 10 years to the age of son after 10 years.

(d) Age of father to the age of son when father was 30 years old.

Q14) Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.

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Mathematics

NCERT Solutions - Mathematics, Class 6

Knowing Our Numbers

Whole Numbers

Playing With Numbers

Basic Geometrical Ideas

Understanding Elementary Shapes

Integers

Fractions

Decimals

Data Handling

Mensuration

Algebra

Ratio and Proportion

Symmetry

Exercise 12.1

Exercise 12.2

Exercise 12.3

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Race To Space

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