Ratio and Proportion (Mathematics) Class 6 - NCERT Questions

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?

(A) The ratio of number of girls to that of boys =

(B) The ratio of number of girls to total number of students =

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.

Total number of students = 30

Number of students like football = 6

Number of students like cricket = 12

Thus, number of students like tennis = 30 - 6 - 12 = 12

(A) The ratio of number of students liking football to that of tennis =

(B) The ratio of number of students liking cricket to that of total 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.

(A) The ratio of number of triangles to that of circles =

(B) The ratio of number of squares to that of all figures =

(C) The ratio of number of circles to that of all figures =

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.

SOLUTION: We know that, speed =

Speed of Hamid =

Speed of Akhtar =

∴ The ratio of speed of Hamid to that of Akhtar =

Fill in the following blanks :

[Are these equivalent ratios?]

In order to get the first missing number, we consider the fact that 18 = 3 × 6, *i.e.*, we get 6 when we divide 18 by 3. This indicates that to get the missing number of the second ratio, 15 must also be divided by 3.

When we divide, we get 15 ÷3 = 5. Hence, the second ratio is

Similarly, to get the third ratio, we multiply both terms of the second ratio by 2. Hence, the third ratio is

And to get the fourth ratio, we multiply both terms of the second ratio by 5. Hence, the fourth ratio is

∴

Yes, these are 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

(A) The ratio of 81 to 108

(B) The ratio of 98 to 63 =

(C) The ratio of 33 km to 121 km

(D) The ratio of 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 Re. 1

(D) 500 ml to 2 litres

(A) 1.5 hours = 1.5 × 60 minutes

= 90 minutes[∵ 1 hour = 60 minutes]

Now, the ratio of 30 minutes to 1.5 hours

= 30 minutes : 1.5 hours

= 30 minutes : 90 minutes =

(B) 1.5 m = 1.5 × 100 cm = 150 cm

[∵ 1 m = 100 cm]

Now, the ratio of 40 cm to 1.5 m

= 40 cm : 1.5 m

= 40 cm : 150 cm =

(C) Re. 1 = 100 paise

Now, the ratio of 55 paise to Re. 1

= 55 paise : Re. 1 = 55 paise : 100 paise

(D) 2 litres = 2 × 1000 ml = 2000 ml

[∵ 1 litre = 1000 ml]

Now, the ratio of 500 ml to 2 litres

= 500 ml : 2 litres

= 500 ml : 2000 ml =

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.

Total earning of Seema = Rs. 1,50,000 and savings = Rs. 50,000

∴ Money spent by her

= Rs. 1,50,000 - Rs. 50,000 = Rs. 1,00,000

(A) The ratio of money earned to the money saved by Seema =

(B) The ratio of money saved to the money spent by Seema =

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

SOLUTION:The ratio of number of teachers to that of students =

Q 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.

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

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

Total number of students in the college = 4320

Number of girls = 2300

Therefore, number of boys = 4320 - 2300

= 2020

(A) The ratio of number of girls to the total number of students

(B) The ratio of number of boys to that of girls

(C) The ratio of 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.

Total number of students = 1800

Number of students who opted basketball = 750

Number of students who opted cricket = 800

Therefore, number of students who opted table tennis = 1800 - (750 + 800) = 250

(A) The ratio of number of students who opted basketball to that who opted table tennis

(B) The ratio of number of students who opted cricket to that who opted basketball

(C) The ratio of 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.

SOLUTION: Cost of a dozen pens (12 pens) = Rs. 180

∴ Cost of 1 pen =

Cost of 8 ball pens = Rs. 56

∴ Cost of 1 pen =

Hence, the ratio of cost of one pen to that of one 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.

Ratio of breadth to length of the hall

∴ Other equivalent ratios are

Thus,

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

SOLUTION: The ratio of dividing pens between Sheela and Sangeeta = 3 : 2.

∴The two parts are 3 and 2.

Sum of the parts = 3 + 2 = 5

Therefore, part of Sheela = of total pens

= × 20 = 12 pens

And part of Sangeeta = of total pens

= × 20 = 8 pens

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: The ratio of the age of Shreya to that of Bhoomika =

Thus, Rs. 36 will be divided between Shreya and Bhoomika in the ratio of 5 : 4.

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.

(A) The ratio of father's present age to that of son

(B) When son was 12 years old, *i.e.*, 2 years ago, then father was (42 - 2) = 40 years old.

Therefore, the required ratio of their ages

(C) Age of father after 10 years

= (42 + 10) years = 52 years

Age of son after 10 years

= (14 + 10) years = 24 years

Therefore, the required ratio of their ages

(D) When father was 30 years old, *i.e.*, 12 years ago, then son was (14 - 12) = 2 years old.

Therefore, the required ratio of their ages

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

(A) Ratio of 15 and 45 = 15 : 45 =

Ratio of 40 and 120 = 40 : 120 =

Since, 15 : 45 = 40 : 120

Therefore, 15, 45, 40, 120 are in proportion.

(B) Ratio of 33 and 121 = 33 : 121 =

= 3:11

Ratio of 9 and 96 = 9 : 96 = = 3 : 32

Since, 33 : 121 ≠9 : 96

Therefore, 33, 121, 9, 96 are not in proportion.

(C) Ratio of 24 and 28 = 24 : 28 = = 6 : 7

Ratio of 36 and 48 = 36 : 48 = = 3 : 4

Since, 24 : 28 ≠36 : 48

Therefore, 24, 28, 36, 48 are not in proportion.

(D) Ratio of 32 and 48 = 32 : 48 = = 2 : 3

Ratio of 70 and 210 = 70 : 210 = = 1 : 3

Since, 32 : 48 ≠70 : 210

Therefore, 32, 48, 70, 210 are not in proportion.

(E) Ratio of 4 and 6 = 4 : 6 = = 2 : 3

Ratio of 8 and 12 = 8 : 12 = = 2 : 3

Since, 4 : 6 = 8 : 12

Therefore, 4, 6, 8, 12 are in proportion.

(F) Ratio of 33 and 44 = 33 : 44 = = 3 : 4

Ratio of 75 and 100 = 75 : 100 = = 3 : 4

Since, 33 : 44 = 75 : 100

Therefore, 33, 44, 75, 100 are in proportion.

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

**(A) True**

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

(A) 40 persons : 200 persons

& Rs. 15 : Rs. 75 = = 1 : 5

⇒ 40 persons : 200 persons = Rs. 15 : Rs. 75

Hence, the statement is true.

(B) 7.5 litres : 15 litres = = 1 : 2

5 kg : 10 kg = = 1 : 2

∴ 7.5 litres : 15 litres = 5 kg : 10 kg

Hence, the statement is true.

(C) 99 kg : 45 kg = = 11 : 5

Rs. 44 : Rs. 20 = = 11 : 5

∴ 99 kg : 45 kg = Rs. 44 : Rs. 20

Hence, the statement is true.

(D) 32 m : 64 m = = 1 : 2

6 sec : 12 sec = = 1 : 2

∴ 32 m : 64 m = 6 sec : 12 sec

Hence, the statement is true.

(E) 45 km : 60 km = = 3 : 4

12 hours : 15 hours = = 4 : 5

∴ 45 km : 60 km ≠12 hours : 15 hours

Hence, the statement is not true.

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 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 ml : 2.5 litre and Rs. 4 : Rs. 50

(A) 25 cm : 1 m = 25 cm : (1 × 100) cm

= 25 cm : 100 cm = = 1 : 4

Rs. 40 : Rs. 160 = = 1 : 4

Since the ratios are equal, therefore these are in proportion.

Middle terms are 1 m and Rs. 40

and extreme terms are 25 cm and Rs. 160.

(B) 39 litres : 65 litres = = 3 : 5

6 bottles : 10 bottles = = 3 : 5

Since the ratios are equal, therefore these are in proportion.

Middle terms are 65 litres and 6 bottles and extreme terms are 39 litres and 10 bottles.

(C) 2 kg : 80 kg = = 1 : 40

25 g : 625 g = = 1 : 25

Since the ratios are not equal, therefore these are not in proportion.

(D) 200 ml : 2.5 litres = 200 ml : (2.5 × 1000) ml

= 200 ml : 2500 ml = = 2 : 25

Rs. 4 : Rs. 50 = = 2 : 25

Since the ratios are equal, therefore these are in proportion.

Middle terms are 2.5 litres and Rs. 4

and extreme terms are 200 ml and Rs. 50.

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

SOLUTION: Cost of 7 m of cloth = Rs. 294

∴ Cost of 1 m of cloth = Rs. = Rs. 42

∴ Cost of 5 m of cloth = Rs. 42 × 5 = Rs. 210

Thus, the cost of 5 m of cloth is Rs. 210.

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

SOLUTION: Earning of 10 days = Rs. 1500

∴ Earning of 1 day = Rs. = Rs. 150

∴ Earning of 30 days = Rs. 150 × 30 = Rs. 4500

Thus, the earning of 30 days is Rs. 4,500.

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.

Rain fall in 3 days = 276 mm

∴ Rain fall in 1 day = mm = 92 mm

∴ Rain fall in 7 days = 92 × 7 mm = 644 mm

Thus, the rain fall in one full week is 644 mm.

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?

(A) Cost of 5 kg of wheat = Rs. 30.50

∴ Cost of 1 kg of wheat =

= Rs. 6.10

∴ Cost of 8 kg of wheat = Rs. 6.10 × 8 = Rs. 48.80

(B) From Rs. 30.50, quantity of wheat can be purchased = 5 kg

∴ From Re. 1, quantity of wheat can be purchased =

∴ From Rs. 61, quantity of wheat can be purchased

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?

SOLUTION:Temperature dropped in last 30 days = 15 degrees

Temperature dropped in 1 day

Temperature will drop in next 10 days

Thus, 5 degree celsius temperature will drop in next 10 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?

SOLUTION:Rent paid for 3 months = Rs. 7500

∴ Rent paid for 1 month =

∴ Rent paid for 12 months = Rs. 2500 × 12

= Rs. 30,000

Thus, the total rent of one year is Rs. 30,000.

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

SOLUTION:Cost of 4 dozens bananas = Rs. 60

[∵ 4 dozens = 4 × 12 = 48]

From Rs. 60, number of bananas can be purchased = 48

∴ From Re. 1, number of bananas can be purchased =

∴ From Rs. 12.50, number of bananas can be purchased

Thus, 10 bananas can be purchased for Rs. 12.50.

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

SOLUTION:The weight of 72 books = 9 kg

∴ The weight of 1 book

∴ The weight of 40 book =

Thus, the weight of 40 books is 5 kg.

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?

SOLUTION:For covering 594 km, required diesel = 108 litres

∴ For covering 1 km, required diesel

∴ For covering 1650 km, required diesel

Thus, 300 litres of 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?

SOLUTION:Cost of 10 pens for Raju = Rs. 150

∴ Cost of 1 pen for Raju =

Cost of 7 pens for Manish = Rs. 84

∴ Cost of 1 pen for Manish =

Thus, Manish 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?

SOLUTION:Runs made by Anish in 6 overs = 42

∴ Runs made by Anish in 1 over

Runs made by Anup in 7 overs = 63

∴ Runs made by Anup in 1 over

Thus, Anup made more runs per over.