Q.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?

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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Number of girls = 20 girls

Number of boys = 15 boys

Total number of students = 20 + 15 = 35

(a) Ratio of number of girls to number of boys
= 20 / 15 = 4 : 5

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

Q.2 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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

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 number of students liking football to the number of students liking tennis

= 6 / 12 = 1 : 2

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

= 12 / 30 = 2 : 5

Q.3 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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Number of triangles = 3

Number of circles = 2

Number of squares = 2

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

= 3 : 2

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

= 2 : 7

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

= 2 : 7

Q.4 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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Distance travelled by Hamid = 9 km.

Distance travelled by Akhtar = 12 km.

Speed of Hamid = 9 km per hour

per hour Speed of Akhtar = 12 km per hour

Ratio of speed of Hamid to the speed of Akhtar

= 9 / 12 = 3 : 4

Q.6 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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

(a) 81 to 108 = \(\frac{81}{108} = \frac{81÷27}{108÷27} = \frac{3}{4} \)

(b) 98 to 63 = \(\frac{98}{63} = \frac{98÷7}{63÷7} = \frac{14}{9} \)

(c) 33 km to 121 km = \(\frac{33 km}{121 km} = \frac{33÷11}{121÷11} = \frac{3}{11} \)

Q.7 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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

(a) 30 minutes to 1.5 hours

1.5 hour = 1.5 × 60 = 90 min

Required ratio = \(\frac{30 min}{90 min} = \frac{30÷30}{90÷30} = \frac{1}{3} \)

= 1 : 3

(b) 40 cm to 1.5 m

1.5 m = 150 cm

Required ratio = \(\frac{40 cm}{150 cm} = \frac{40÷10}{150÷10} = \frac{4}{15} \) = 4 : 15

(c) 55 paise to Rs 1

Rs 1 = 100 paise

Required ratio = \(\frac{55 paise}{100 paise} = \frac{55÷5}{100÷5} = \frac{11}{10} \) = 11 : 20

(d) 500 ml to 2 litres

2 litre = 2000 ml

Required ratio = \(\frac{500 cm}{2000 cm}= \frac{500÷500}{2000÷500} = \frac{1}{4} \) = 1 : 4

Q.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

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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Money earned by Seema = Rs 150000

Money saved by her = Rs 50000

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

(a) Ratio of money earned to money saved

=\(\frac{15000}{5000} = \frac{15000÷5000}{5000÷5000} = \frac{3}{1} \)

= 3 : 1

(b) Ratio of money saved to money spent

=\(\frac{5000}{10000} = \frac{5000÷5000}{10000÷5000} = \frac{1}{2} \)

= 1 : 2

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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Number of teachers in a school = 102

Number of students in a school = 3300

Ratio of number of teachers to the number of students
\(\frac{102}{3300} = \frac{102÷6}{3300÷6} = \frac{17}{550} \)

= 17 : 550

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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Total number of students = 4320

Number of girls = 2300

Number of boys = 4320 – 2300 = 2020

(a) Ratio of number of girls to the total number of students

= \(\frac{2300}{4320} = \frac{2300÷20}{4320÷20} = \frac{115}{216} \)

= 115 : 216

(b) Ratio of number of boys to the number of girls
= \(\frac{2020}{2300} = \frac{2020÷20}{2300÷20} = \frac{101}{115} \)

= 101 : 115

(c) Ratio of number of boys to the total number of students

= \(\frac{2020}{4320} = \frac{2020÷20}{4320÷20} = \frac{101}{216} \)

= 101 : 216

Q.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.

(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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

(a) Ratio of number of students who opted basketball to the number of students who opted table tennis

\(= \frac{750}{250} = \frac{3}{1} \) = 3 : 1

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

=\frac{800}{750} = \frac{800÷50}{750÷50} = \frac{16}{15} = 16 : 15 \)

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

=\(\frac{750}{1800} = \frac{750÷150}{1800÷150} = \frac{5}{12} \)

= 5 : 12

Q.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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Cost of a dozen pens = Rs 180

Cost of 1 pen = \(\frac{180}{12} = Rs 15 \)

Cost of 8 ball pens = Rs 56

Cost of 1 ball pen = \(\frac{56}{8} = Rs 7 \)

Hence, required ratio is = 15 : 7

Q.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.

Breadth of the hall (in metres) \(\rightarrow 10 \square 40 \)

Length of the hall (in metres) \(\rightarrow 25 50 \square \)

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

(i) Length = 50 m

\(\frac{Breadth}{length} = \frac{\square }{50} = \frac{2}{5} \)

By cross multiplication

5× breadth = 50 × 2

Breadth =\(\frac{(50 × 2)}{5} = 20 m \)

(ii) Breadth = 40 m

\(\frac{breadth}{length} = \frac{40}{Length} = \frac{2}{5} \)

By cross multiplication

2 × Length = 40 × 5

Length =\(\frac{(40 × 5)}{2} = 100 \)

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Let , sheela gets 3x pens

Sangeeta gets 2x pens

Sum of pens = 20 pens

3x + 2x = 20

=> 5x = 20

=> x = \(\frac{20}{5} = 4 \)

sheela gets 3x pens = 3×4 = 12 pens

Sangeeta gets 2x pens = 2×4 = 8 pens

Q.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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Ratio of ages \(= \frac{15}{12} = \frac{5}{4} \) = 5 : 4

Hence, mother wants to divide Rs 36 in the ratio of 5: 4

Terms of 5: 4 are 5 and 4

Sum of these terms = 5 + 4 = 9

Here Shreya will get \(\frac{5}{9} \) of total money and

Sangeeta will get \(\frac{4}{9} \) of total money

The amount Shreya get = \(\frac{5}{9} × 36 \) = 20

The amount Sangeeta get = \(\frac{4}{9} × 36 \) = 16

Therefore Shreya will get Rs 20 and Sangeeta will get Rs 16

Q.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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

(a) Present age of father = 42 years

Present age of son = 14 years

Required ratio \(\frac{42}{14} = \frac{3}{1} = 3 : 1 \)

(b) The son was 12 years old 2 years ago. So the age of father 2 years ago will be

= 42 – 2 = 40 years

Required ratio = \(\frac{40}{12} = \frac{40÷4}{12÷4} = \frac{10}{3} = 10 : 3 \)

(c) After ten years age of father = 42 + 10 = 52 years

After 10 years age of son = 14 + 10 = 24 years

Required ratio = \(\frac{52}{24} = \frac{52÷4}{24÷4} = \frac{13}{6} = 13 : 6 \)

(d) 12 years ago, age of father was 30

At that time age of son = 14 – 12 = 2 years

Required ratio = \(\frac{30}{2} \) = 15 = 15 :1

Q.5 Fill in the following blanks:

\(\frac{15}{18} =\frac{\square }{6} = \frac{10}{\square }= \frac{\square }{30} \) [Are these equivalent ratios?]

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

\(\frac{15}{18} = \frac{15÷3}{18÷3} = \frac{5}{6} \)

\(\frac{5}{6} = \frac{5×2}{6×2} = \frac{10}{12} \)

\(\frac{5}{6} = \frac{5×5}{6×5} = \frac{25}{30} \)

Yea these are equivalent ratios

Q.1 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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

(a) 15, 45, 40, 120

\(\frac{15}{45} = \frac{1}{3} \)

\(\frac{40}120} = \frac{1}{3} \)

Hence, 15: 45 = 40:120

\(\therefore \)These are in a proportion

(b) 33, 121, 9, 96

\(\frac{33}{121} = \frac{3}{11} \)

\(\frac{9}{96} = \frac{3}{32} \)

Hence 33:121 \(\neq \)9: 96

\(\therefore \)These are not in a proportion

(c) 24, 28, 36, 48

\(\frac{24}{28} = \frac{6}{7} \)

\(\frac{36}{48} = \frac{3}{4} \)

Hence, 24: 28 \(\neq \)36:48

\(\therefore \) These are not in a proportion

(d) 32, 48, 70, 210

\(\frac{32}{48} = \frac{2}{3} \)

\(\frac{70}{210} = \frac{1}{3} \)

Hence, 32: 48 \(\neq \)70: 210

\(\therefore \)These are not in a proportion

(e) 4, 6, 8, 12

\(\frac{4}{6} = \frac{2}{3} \)

\(\frac{8}{12} = \frac{2}{3} \)

Hence 4: 6 = 8: 12

\(\therefore \) These are in a proportion

(f) 33, 44, 75, 100

\(\frac{33}{44} = \frac{3}{4} \)

\(\frac{75}{100} = \frac{3}{4} \)

Hence, 33:44 = 75: 100

\(\therefore \)These are in a proportion

Q.2 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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

(a) 16: 24 :: 20: 30

\(\frac{16}{24} = \frac{2}{3} \)

\(\frac{20}{30} = \frac{2}{3} \)

Hence, 16: 24 = 20: 30

Therefore True

(b) 21: 6:: 35: 10

\(\frac{21}{6} = \frac{7}{2} \)

\(\frac{35}{10} = \frac{7}{2} \)

Hence, 21: 6 = 35: 10

Therefore True

(c) 12: 18 :: 28: 12

\(\frac{12}{18} = \frac{2}{3} \)

\(\frac{28}{12} = \frac{7}{3} \)

Hence, 12: 18 \(\neq \)28:12

Therefore False

(d) 8: 9:: 24: 27

\(\frac{24}{27} = \frac{8}{9} \)

Hence, 8: 9 = 24: 27

Therefore True

(e) 5.2: 3.9:: 3: 4

\(\frac{5.2}{3.9} = \frac{4}{3} \)

Hence, 5.2: 3.9 \(\neq \) 3: 4

Therefore False

(f) 0.9: 0.36:: 10: 4

\(\frac{0.9}{0.36} = \frac{10}{4} \)

Hence, 0.9: 0.36 = 10: 4

Therefore True

Q.3 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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

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

\(\frac{40}{200} = \frac{1}{5} \)

\(\frac{15}{75} = \frac{1}{5} \)

Hence, True

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

\(\frac{7.5}{15} = \frac{1}{2} \)

\(\frac{5}{10} = \frac{1}{2} \)

Hence, True

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

\(\frac{99}{45} = \frac{11}{5} \)

\(\frac{44}{20} = \frac{11}{5} \)

Hence, True

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

\(\frac{32}{64} = \frac{1}{2} \)

\(\frac{6}{12} = \frac{1}{2} \)

Hence, True

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

\(\frac{45}{60} = \frac{3}{4} \)

\(\frac{12}{15} = \frac{4}{5} \)

Hence, False

Q.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 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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

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

1 m = 100 cm

\(\frac{25cm}{100cm} = \frac{1}{4} \)

\(\frac{40}{160} = \frac{1}{4} \)

Yes, these are in a proportion

Middle terms are 1 m, Rs 40 and Extreme terms are 25 cm, Rs 160

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

\(\frac{39}{65} = \frac{3}{5} \)

\(\frac{6}{10} = \frac{3}{5} \)

Yes, these are in a proportion

Middle terms are 65 litres, 6 bottles and Extreme terms are 39 litres, 10 bottles

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

\(\frac{2}{80} = \frac{1}{40} \)

\(\frac{25}{625} = \frac{1}{25} \)

No, these are not in a proportion

(d) 200 mL : 2.5 litre and ? 4 : ? 50

2.5 litre = 2500 ml

\(\frac{200}{2500} = \frac{2}{25} \)

\(\frac{4}{50} = \frac{2}{25} \)

Yes, these are in a proportion

Middle terms are 2.5 litres, Rs 4 and Extreme terms are 200 ml, Rs 50

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

In 10 days Ekta earn Rs 1500

In 1 days Ekta will earn Rs 1500/10
In 30 days Ekta will earn Rs\(\frac{1500}{10} x 30 = Rs4500 \)

Thus the money earned by Ekta in 30 days = Rs 4500

Q.3 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.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

In last 3 days the rain falls = 276 mm .

In 1 day the rain falls = 276/3mm.

in 7 days the rain will fall = 92 x 7 mm.

= 92 x 7 mm = 644 mm = 64.4 cm

Thus, the amount of rain fall in week = 64.4 cm.

Q.4 Cost of 5 kg of wheat is Rs 91.50.

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

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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

(a) Cost of 5 kg of wheat = Rs 91.50

Cost of 1 kg of wheat = Rs 91.50/5

Cost of 8 kg of wheat = Rs ( 18.3 x 8)

= Rs 146.40

Thus, the required cost = Rs 146.40

(b) Wheat purchased in Rs 91.50 = 5 kg

Wheat purchased in Rs 1 = (5 / 91.50 )kg

So, wheat purchased in Rs 183 = (5 / 91.50) × 183

= 10 kg

Q.5 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?

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Temperature drop in 30 days = 15° C

Temperature drop in 1 day = 15 / 30

= (1 / 2)° C

So, temperature drop in next 10 days = (1 / 2) × 10

= 5° C

\(\therefore \) The temperature drop in the next 10 days will be 5° C

Q.6 Shaina pays Rs 15000 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Amount of rent paid in 3 months = Rs 7500

Amount of rent paid in 1 month = Rs 7500/3

Amount of rent paid in 12 months = Rs ( 2500 x 12)
= Rs 30,000

Thus the required amount of rent paid in 1 year = Rs 30,000.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Number of bananas bought in Rs180 = 4 dozens

= 4 × 12 = 48 bananas

Number of bananas bought in Rs 1 = \(\frac{48}{180} \)

So, number of bananas bought in Rs 90 = \(\frac{48}{180} \) × 90 = 24 bananas

\(\therefore \) 24 bananas can be purchased in Rs 90

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Weight of 72 books = 9 kg

Weight of 1 book = \(\frac{9}{72} = \frac{1}{8} \)

So, weight of 40 books = \(\frac{1}{8} \) × 40 = 5 kg

\(\therefore \)Weight of 40 books is 5 kg

Q.9 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?

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Diesel required for 594 km = 108 litres

Diesel required for 1 km =\(\frac{108}{594} = \frac{2}{11} \)

So, diesel required for 1650 km = \(\frac{2}{11} × 1650 = 300 litres \)

\(\therefore \) Diesel required by the truck to cover a distance of 1650 km is 300 litres

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

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Pens purchased by Raju in Rs 150 = 10 pens
Cost of 1 pen = \(\frac{150}{10} = Rs 15 \)

Pens purchased by Manish in Rs 84 = 7 pens

Cost of 1 pen = \(\frac{84}{7} \)

\(\therefore \) Pens purchased by Manish are cheaper than Raju

NCERT Solutions for Class 6 Maths Chapter 12 Ratio And Proportion

Answer :

Runs made by Anish in 6 overs = 42

Runs made by Anish in 1 over = \(\frac{42}{7} \) = 7

Runs made by Anup in 7 overs = 63

Runs made by Anup in 1 over = \(\frac{63}{7} \)

\(\therefore \) Anup scored more runs than Anish.

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