Chapter 12: Ratio and Proportion

Q11Written answer

Out of 1800 students in a school, 750 opted for basketball, 800 opted for cricket, and the remaining opted for table tennis. If a student can opt for only one game, find the ratio of

(a) The number of students who opted for basketball to the number of students who opted for table tennis.

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

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

Show solutionHide solution

Worked solution

Given,

Number of students in the school = 1800

The number of students who opted for basketball = 750

The number of students who opted for cricket = 800

The number of students who opted for table tennis = 1800 – (750 + 800) = 1800 – 1550 = 250

(a) Ratio of the number of students who opted for basketball to the number of students who opted for table tennis = 750 / 250 = 3 / 1

(b) Ratio of the number of students who opted for cricket to the number of students who opted for basketball

= 800 / 750 = 16 / 15

(c) Ratio of the number of students who opted for basketball to the total number of students

= 750 / 1800 = 25 / 60 = 5 / 12

Q12Written answer

Cost of a dozen pens is ₹ 180, and the cost of 8 ball pens is ₹ 56. Find the ratio of the cost of a pen to the cost of a ball pen.

Show solutionHide solution

Worked solution

Cost of a dozen pens = ₹ 180

Cost of 1 pen = 180 / 12

= ₹ 15

Cost of 8 ball pens = ₹ 56

Cost of 1 ball pen = 56 / 8

= ₹ 7

Hence, the required ratio is 15 / 7.

Q13Written answer

Consider the statement: The 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.

Breadth of the hall (in metres)	10		40
Length of the hall (in metres)	25	50

Show solutionHide solution

Worked solution

(i) Length = 50 m

Breadth / 50 = 2 / 5

By cross multiplication

5× breadth = 50 × 2

Breadth = (50 × 2) / 5

= 100 / 5

= 20 m

(ii) Breadth = 40 m

40 / Length = 2 / 5

By cross multiplication

2 × Length = 40 × 5

Length = (40 × 5) / 2

Length = 200 / 2

Length = 100 m

Q14Written answer

Divide 20 pens between Sheela and Sangeeta in a ratio of 3:2.

Show solutionHide solution

Worked solution

Terms of 3:2 = 3 and 2

The sum of these terms = 3 + 2

= 5

Now, Sheela will get 3 / 5 of the total pens, and Sangeeta will get 2 / 5 of the total pens

Number of pens with Sheela = 3 / 5 × 20

= 3 × 4

= 12

Number of pens with Sangeeta = 2 / 5 × 20

= 2 × 4

= 8

Q15Written answer

Mother wants to divide ₹ 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If the age of Shreya is 15 years and the age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get.

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.1 - 3

Show solutionHide solution

Worked solution

Ratio of ages = 15 / 12

= 5 / 4

Hence, the mother wants to divide ₹ 36 in the ratio of 5:4

Terms of 5:4 are 5 and 4

The sum of these terms = 5 + 4

= 9

Here, Shreya will get 5 / 9 of the total money, and Sangeeta will get 4 / 9 of the total money

The amount Shreya get = 5 / 9 × 36

= 20

The amount Sangeeta get = 4 / 9 × 36

= 16

Therefore, Shreya will get ₹ 20, and Sangeeta will get ₹ 16.

Q16Written answer

Present age of the father is 42 years, and that of his son is 14 years. Find the ratio of

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

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

Show solutionHide solution

Worked solution

(a) Present age of father = 42 years

Present age of son = 14 years

Required ratio 42 / 14

= 3 / 1

(b) 2 years ago, the son was 12 years old. So, 2 years ago, the age of the father was

= 42 – 2 = 40 years

Required ratio = 40 / 12 = (4 × 10) / (4 × 3) = 10 / 3

(c) After ten years, the age of the father = 42 + 10 = 52 years

After 10 years, the age of the son = 14 + 10 = 24 years

Required ratio = 52 / 24 = (4 × 13) / (4 × 6)

= 13 / 6

(d) 12 years ago, the age of the father was 30

At that time, the age of the son = 14 – 12

= 2 years

Required ratio = 30 / 2 = (2 × 15) / 2

= 15 / 1

My Cart

Your Cart 0

Exercise 12.1