## NCERT Class 6 Mathematics Twelfth Chapter Ratio And Proportion Exercise 12.1 Solution

EXERCISE 12.1

**(1) There are 20 girls and 15 boys in a class. **

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

Ans: 20 : 15

= 4 : 3

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

Ans: 20 : 35

= 4 : 7

**(2) Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of **

Here, number of liking tennis = 30 – (12 + 6) = 12 students.

(a) Number of students liking football to number of students liking tennis.

Ans: 6 : 12

= 1 : 2

(b) Number of students liking cricket to total number of students.

Ans: 12 : 30

= 2 : 5

**(3) See the figure and find the ratio of **

(a) Number of triangles to the number of circles inside the rectangle.

Ans: 3 : 2

(b) Number of squares to all the figures inside the rectangle.

Ans: 2 : 7

(c) Number of circles to all the figures inside the rectangle.

Ans: 2 : 7

**(4) Distances travelled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the ratio of speed of Hamid to the speed of Akhtar. **

Ans: 9 : 12

= 3 : 4

**(5) Fill in the following blanks: **

**(6) Find the ratio of the following: **

(a) 81 to 108

Solution: 81 : 108

= (81 ÷ 27) : (108 ÷ 27)

= 3 : 4

(b) 98 to 63

Solution: 98 : 63

= (98 ÷ 7) : (63 ÷ 7)

= 14 : 9

(c) 33 km to 121 km

Solution: 33 : 121

= (33 ÷ 11) : (121 ÷ 11)

= 3 : 11

(d) 30 minutes to 45 minutes

Solution: 30 : 45

= (30 ÷ 15) : (45 ÷ 15)

= 2 : 3

**(7) Find the ratio of the following: **

(a) 30 minutes to 1.5 hours

Solution: Here, 1.5 hours = 90 minutes

∴ 30 : 90

= (30 ÷ 30) : (90 ÷ 30)

= 1 : 3

(b) 40 cm to 1.5 m

Solution: 1.5 m = 105 cm

∴ 40 : 150

= (40 ÷ 10) : (150 ÷ 10)

= 4 : 15

(c) 55 paise to Rs 1

Solution: Here, Rs 1 = 100 paise

∴ 55 : 100

= (55 ÷ 5) : (100 ÷ 5)

= 11 : 20

(d) 500 mL to 2 litres

Solution: 2 litres = 2000

∴ 500 : 2000

= (500 ÷ 500) : (2000 ÷ 500)

= 1 : 4

**(8) In a year, Seema earns Rs 1,50,000 and saves Rs 50,000. Find the ratio of **

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

Solution: 150000 : 50000

= (150000 ÷ 50000) : (50000 ÷ 50000)

= 3 : 1

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

Solution: Here, Seema spends money = Rs (150000 – 50000) = Rs 100000

∴ 50000 : 100000

= (50000 ÷ 50000) : (100000 ÷ 50000)

= 1 : 2

**(9) There are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students. **

Solution: 102 : 3300

= (102 ÷ 3) : (3300 ÷ 3)

= 17 : 550

**(10) In a college, out of 4320 students, 2300 are girls. Find the ratio of **

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

Solution: 2300 : 4320

= (2300 ÷ 20) : (4320 ÷ 20)

= 115 : 216

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

Solution: Here, the number of boys = (4320 – 2300) = 2020

∴ 2020 : 2300

= (2020 ÷ 20) : (2300 ÷ 20)

= 101 : 115

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

Solution : 2020 : 4320

= (2020 ÷ 20) : (4320 ÷ 20)

= 101 : 216

**(11) 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.

Solution: Here, the number of students whose are playing tennis = 1800 – (750 + 800) = 1800 – 1550 = 250

∴ 750 : 250

= (750 ÷ 250) : (250 ÷ 250)

= 3 : 1

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

Solution: 800 : 750

= (800 ÷ 50) : (750 : 50)

= 16 : 15

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

Solution: 750 : 1800

= 5 : 12

**In case you are missed :- NCERT Solution for Knowing Our Numbers Exercise 1.3**

**(12) Cost of a dozen pens is Rs 180 and cost of 8 ball pens is Rs 56. Find the ratio of the cost of a pen to the cost of a ball pen. **

Solution: Here, if cost of 12 pen is = Rs 180

∴ cost of 1 pen = Rs (180 ÷ 12) = Rs 15

If cost of 8 ball is = Rs 56

∴ cost of 1 pen is = Rs (56 ÷ 8) = Rs 7

∴ 15 : 7

**(13) 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. **

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

Solution: The sum of two ratio = (3 + 2) = 5

**(15) Mother wants to divide Rs 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. **

Solution: Ratio of their age = 15 : 12 = 5 : 4

The sum of the ratio = (5 + 4) = 9

**(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.

Solution: 42 : 14

= (42 ÷ 14) : (14 ÷ 14)

= 3 : 1

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

Solution: When Son was 12 years old then his father was (42 – 2) = 40 years old.

∴ 40 : 12

= (40 ÷ 4) : (12 ÷ 4)

= 10 : 3

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

Solution: After 10 years father and son’s age will be 52 years and 24 years.

∴ 52 : 24

= (52 ÷ 4) : (24 ÷ 4)

= 13 : 6

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

Solution: When father was 30 years old the age of son was (14 – 12) = 2 years.

∴ 30 : 2

= (30 ÷ 2) : (2 ÷ 2)

= 15 : 1

**In case you are missed :- Next Chapter Exercise Solution**