Solution of Chapter 12. Ratio and Proportion (NCERT - Mathematics Book)

There are 20 girls and 15 boys in a class.

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

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

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 number of students liking tennis.

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

See the figure and find the ratio of

(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.

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

Fill in the following blanks:

[Are these equivalent ratios?]

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.

Find the ratio of the following:

(a) 30 minutes to 1.5 hours

(b) 40 cm to 1.5 m

(c) 55 paise to Rs 1

(d) 500 ml to 2 litres

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.

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

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

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.

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

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

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.

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.

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

Mother wants to divide Rs 36 between her daughters Shreya and Bhoomika in the ratio of their ages. Ig age of Shreya is 15 years and age of Bhoomika is 12 years. Find how much Shreya and Bhoomika will get.

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.

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

Write True (T) or False (F) against each of the following statements:

(a) 16 : 24 : : 20 : 30

(b) 21 : 6 : : 35 : 10

(c) 12 : 18 : : 28 : 12

(d) 8 : 9 : : 24 : 27

(e) 5.2 : 3.9 : : 3 : 4

(f) 0.9 : 0.36 : : 10 : 4

Are the following statements true?

(a) 40 persons : 200 persons = Rs. 15 : Rs. 75

(b) 7.5 litres : 15 litres = 5 kg ; 10 kg

(c) 99 kg : 45 kg = Rs. 44 : Rs. 20

(d) 32 m : 64 m = 6 sec : 12 sec

(e) 45 km : 60 km = 12 hours : 15 hours.

Determine if the follow ratios form a proportion. Also, write the middle terms and extreme terms where the ratio forms a proportion.

(a) 25 cm : 1 m and Rs. 40 : Rs. 160

(b) 39 litres : 65 litres and 6 bottles : 10 bottles

(c) 2 kg : 80 kg and 25 g : 625 g

(d) 200 mil : 2.5 litres and Rs. 4 : Rs. 50

If the cost of 7m of cloth is Rs. 294, find the cost of 5 m of cloth.

Ekta earns Rs 1500 in 10 days. How much will she earn in 30 days?

If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.

Cost of 5 kg of wheat is Rs. 30.50.

(a) What will be the cost of 8 kg of wheat?

(b) What quantity of wheat can be purchased in Rs. 61?

The temperature dropped 15 degrees Celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees Celsius will the temperature drop in the next ten days?

Shaina pays Rs. 7500 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?

Cost of 4 dozens bananas is Rs. 60. How many bananas can be purchased for Rs. 12.50?

The weight of 72 books is 9 kg. What is the weight of 40 such books?

A truck required 108 litres of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?

Raju purchases 10 pens for Rs. 150 and Manish buys 7 pens for Rs. 84. Can you say who got the pens cheaper?

Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?