Chapter 12: Ratio and Proportion

Q1Written answer

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?

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Worked solution

Given

Number of girls = 20 girls

Number of boys = 15 boys

Total number of students = 20 + 15

= 35

(a) Ratio of the number of girls to the number of boys = 20 / 15 = 4 / 3

(b) Ratio of the number of girls to the total number of students = 20 / 35 = 4 / 7

Q2Written answer

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

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.1 - 1

(a) The number of students liking football to the number of students liking tennis.

(b) The number of students liking cricket to the total number of students.

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Worked solution

Given

Number of students who like football = 6

Number of students who like cricket = 12

Number of students who like tennis = 30 – 6 – 12

= 12

(a) Ratio of the number of students liking football to the number of students liking tennis

= 6 / 12 = 1 / 2

(b) Ratio of the number of students liking cricket to the total number of students

= 12 / 30

= 2 / 5

Q3Written answer

See the figure and find the ratio of

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.1 - 2

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

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

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

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Worked solution

Given in the figure

Number of triangles = 3

Number of circles = 2

Number of squares = 2

Total number of figures = 7

(a) Ratio of the number of triangles to the number of circles inside the rectangle

= 3 / 2

(b) Ratio of the number of squares to all the figures inside the rectangle

= 2 / 7

(c) Ratio of the number of circles to all the figures inside the rectangle

= 2 / 7

Q4Written answer

The distance travelled by Hamid and Akhtar in an hour is 9 km and 12 km, respectively. Find the ratio of the speed of Hamid to the speed of Akhtar.

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Worked solution

We know that the speed of a certain object is the distance travelled by that object in an hour

Distance travelled by Hamid in one hour = 9 km

Distance travelled by Akhtar in one hour = 12 km

Speed of Hamid = 9 km/hr

Speed of Akhtar = 12 km/hr

The ratio of the speed of Hamid to the speed of Akhtar = 9 / 12 = 3 / 4

Q5Written answer

Fill in the blanks:

15 / 18 = ☐ / 6 = 10 / ☐ = ☐ / 30 [Are these equivalent ratios?]

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Worked solution

15 / 18 = (5 × 3) / (6 × 3)

= 5 / 6

5 / 6 = (5 × 2) / (6 × 2)

= 10 / 12

5 / 6 = (5 × 5) / (6 × 5)

= 25 / 30

Hence, 5, 12 and 25 are the numbers which come in the blanks, respectively.

Yes, all are equivalent ratios.

Q6Written answer

Find the ratio of the following:

(a) 81 to 108

(b) 98 to 63

(c) 33 km to 121 km

(d) 30 minutes to 45 minutes

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Worked solution

(a) 81 / 108 = (3 × 3 × 3 × 3) / (2 × 2 × 3 × 3 × 3)

= 3 / 4

(b) 98 / 63 = (14 × 7) / (9 × 7)

= 14 / 9

(c) 33 / 121 = (3 × 11) / (11 × 11)

= 3 / 11

(d) 30 / 45 = (2 × 3 × 5) / (3 × 3 × 5)

= 2 / 3

Q7Written answer

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

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Worked solution

(a) 30 minutes to 1.5 hours

30 min = 30 / 60

= 0.5 hours

Required ratio = (0.5 × 1) / (0.5 × 3)

= 1 / 3

(b) 40 cm to 1.5 m

1.5 m = 150 cm

Required ratio = 40 / 150

= 4 / 15

(c) 55 paise to ₹ 1

₹ 1 = 100 paise

Required ratio = 55 / 100 = (11 × 5) / (20 × 5)

= 11 / 20

(d) 500 ml to 2 litres

1 litre = 1000 ml

2 litre = 2000 ml

Required ratio = 500 / 2000 = 5 / 20 = 5 / (5 × 4)

= 1 / 4

Q8Written answer

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

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

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

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Worked solution

Money earned by Seema = ₹ 150000

Money saved by her = ₹ 50000

Money spent by her = ₹ 150000 – ₹ 50000 = ₹ 100000

(a) Ratio of money earned to money saved = 150000 / 50000 = 15 / 5

= 3 / 1

(b) Ratio of money saved to money spent = 50000 / 100000 = 5 / 10

= 1 / 2

Q9Written answer

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

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Worked solution

Given

Number of teachers in the school = 102

Number of students in the school = 3300

The ratio of the number of teachers to the number of students = 102 / 3300

= (2 × 3 × 17) / (2 × 3 × 550)

= 17 / 550

Q10Written answer

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) Number of boys to the number of girls.

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

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Worked solution

Given

Total number of students = 4320

Number of girls = 2300

Number of boys = 4320 – 2300

= 2020

(a) Ratio of the number of girls to the total number of students = 2300 / 4320

= (2 × 2 × 5 × 115) / (2 × 2 × 5 × 216)

= 115 / 216

(b) Ratio of the number of boys to the number of girls = 2020 / 2300

= (2 × 2 × 5 × 101) / (2 × 2 × 5 × 115)

= 101 / 115

(c) Ratio of the number of boys to the total number of students = 2020 / 4320

= (2 × 2 × 5 × 101) / (2 × 2 × 5 × 216)

= 101 / 216

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Exercise 12.1