Ncert solutions mathematics class 6 Solutions for Chapter 12 ratio and proportion

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

rectangle.

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

(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.

There are 20 girls and 15 boys in a class.

(a) What is the ratio of number of girls to the number 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.

Distance 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.

Fill in the following blanks:

15 / 18 = ☐ / 6 = 10 / ☐ = ☐ / 30 [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 ₹ 1

(d) 500 ml to 2 litres

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.

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 ₹ 180 and cost of 8 ball pens is ₹ 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 ₹ 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.

Q2) 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

Q3)Are the following statements true?

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

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

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

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

Q4) Determine if the following ratios form a proportion. Also, write the middle terms

and extreme terms where the ratios form a proportion.

(a) 25 cm : 1 m and 40 : 160 (b)39 litres : 65 litres and 6 bottles : 10 bottles

(c) 2 kg : 80 kg and 25 g : 625 g (d) 200 mL : 2.5 litre and 4 : 50

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

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

(a) 25 cm : 1 m and ₹ 40 : ₹ 160

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

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

(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

Q2) Ekta earns 3000 in 10 days. How much will she earn in 30 days?

Q1) If the cost of 7 m of cloth is 1470, find the cost of 5 m of cloth.

Q3) 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.

Q4) Cost of 5 kg of wheat is`91.50.

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

(b) What quantity of wheat can be purchased in 183?

Q5) The temperature dropped 15-degree celsius in the last 30 days. If the rate of

temperature drop remains the same, how many degrees will the temperature

drop in the next ten days?

Q6) Shaina pays 15000 as rent for 3 months. How much does she have to pay for a

the whole year, if the rent per month remains the same?

Q7) Cost of 4 dozen bananas is ` 180. How many bananas can be purchased for

90?

Q10) Raju purchases 10 pens for 150 and Manish buys 7 pens for 84. Can you say

who got the pens cheaper?

Q11)

Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made

more runs per over?

Q8) The weight of 72 books is 9 kg. What is the weight of 40 such books?

Q9) A truck requires 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?

If the cost of 7 m of cloth is ₹ 1470, find the cost of 5 m of cloth.

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 ₹ 91.50.

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

(b) What quantity of wheat can be purchased in ₹ 183?

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

Shaina pays ₹ 15000 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 dozen bananas is ₹ 180. How many bananas can be purchased for ₹ 90?

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

A truck requires 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 ₹ 150 and Manish buys 7 pens for ₹ 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?