# Joy of Mathematics Class 6 Solutions Chapter 7

## Joy of Mathematics Class 6 Solutions Chapter 7 Ratio and Proportion

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Joy of Mathematics Class 6 Book, Chapter 7 Ratio and Proportion. Here students can easily find step by step solutions of all the problems for Ratio and Proportion. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Students will get chapter 7 solutions. Here students will find exercise wise solutions for chapter 7 Exercise 7.1, 7.2, 7.3 and 7.4

Ratio and Proportion Exercise 7.1 Solution :

Question no – (1)

Solution :

 Fraction Ratio Simplify Ratio (a) 4 kg to 12 kg 4/12 4 : 12 1 : 3 (b) 450 g to 1 kg 450/1000 450 : 1000 9 : 20 (c) 50 p to Rs 3 50/300 50 : 300 1 : 6 (d) 40 cm to 2 m 40/200 40 : 200 1 : 5 (e) 20 minutes to 3 hours 20/180 20 : 180 1 : 9 (f) 73 days to an year 73/365 73 : 365 1 : 5

Question no – (2)

Solution :

(a) 20 : 35

= 4 : 7

(b) 40 : 20

= 2 : 1

(c) 1/15 : 1/20

= 1/5 × 60 : 1/20 × 60

= 4 : 3

(d) 2 1/15 : 3 1/15

= 31/15 : 46/15

= 31 : 46

(e) 8 : 12

= 2 : 3

(f) 1/2 : 3/4 : 5/8

= 1/2 × 8 : 3/4 × 8 : 5/8 × 8

= 4 : 6 : 5

(h) 25 : 15

= 5 : 3

Question no – (3)

Solution :

(a) 2.1 m : 90 cm

= 210 : 90 cm

= 21 : 9

= 7 : 3

(b) 10 m : 40 cm

= 1000 : 40

= 100 : 4

= 25 : 1

(c) 5 kg : 400 gm

= 5000 : 400

= 50 : 4

= 25 : 2

(d) 3 hours : 25 second

= (3 × 3600) : 25

= 10800 : 25

= 432 : 1

(e) 3.5 m : 25 m

= 35 : 250

= 7 : 50

(f) 60 paise : 5 Rs

= 60 : 500

= 6 : 50

= 3 : 25

Question no – (4)

Solution :

Good apples = (150 – 30)

= 120

Rotten = 30

Total = 150

(a) Rotten : good

= 30 : 120

= 1 : 4

(c) Good : Total

= 120 : 150

= 4 : 5

(d) Rotten : Total

= 30 : 150

= 1 : 5

Question no – (5)

Solution :

Expenditure,

= (12.450 – 2.490)

= 9960

(a) Savings : Income

= 2490 : 12450

= 249 : 1245

= 1 : 5

(b) Savings : Expenditure

= 2490 : 9960

= 249 : 996

= 1 : 4

Question no – (6)

Solution :

Children

= 60,000 – (25000 + 24000)

= 60,000 – 49000

= 11000

(a) Male : Total

= 250000 : 60,000

= 5 : 12

(b) Female : Total

= 24000 : 60,000

= 24 : 60

= 4 : 10

= 2 : 5

= 24000 : 2500

= 24: 25

(d) Children : Total

= 11000 : 60,000

= 11 : 60

Question no – (7)

Solution :

(a) Lunch break : Total time

= 45 min : 7h

= 45 : (7 × 60)

= 45 : 420

= 3 : 28

(b) Lunch break : Actual working

= 45 : 6h : 15

= 45 : (6 × 60 + 15)

= 45 : 375

= 3 : 25

Question no – (8)

Solution :

Train A cover in 3 h

= (3 × 60)

= 180 km

Train B cover in 3 h

= SA : SB

= 180/3 : 240/3

= 60 : 80

= 3 : 4

Question no – (10)

Solution :

= 6/10 = 3/5 = 15/25

= 18/30 = 303/55

Question no – (11)

Solution :

Weight of Copper

= 7/100 × 30

= 21/10

= 2 : 1 gm

Question no – (12)

Solution :

Total = (4 + 3) unit = 7

= 3 = 18 girls

= 1 = 18/6

= 1 = 18/6 × 4

= 12 boys

Question no – (13)

Solution :

(a) A : B = 3 : 4

B : C – 4.5
————————————-
A : B : C = 3 : 4 : 5

Question no – (14)

Solution :

A : B = 2 : 5 : 5

B : C = 7 : 7 : 9
————————————-
A : B C = 14 : 35 : 45

Question no – (15)

Solution :

Let sides, 3x, 4x, 5x cm

(3x + 4x + 5)

= 84

= 12x + 4x – 5x

= 12x = 84/12

= x = 84/12b

= 7 cm

Sides are, (3 × 7), (4 × 7), (5 × 7)

= 21c,,

= 28cm

= 35 cm

Question no – (16)

Solution :

Football = 200 – (44 + 66)

= 200 – 110

= 90

(a) Cricket : Hockey

= 44 : 66

= 4 : 6

= 2 : 3

(b) Hockey

= 66 : 90

= 44 : 90

= 11 : 5

(c) Cricket : Total

= 44 : 200

= 22: 100

= 11 : 50

Question no – (17)

Solution :

(a) 2 : 5 and 3: 7

= 2/5 < 3/7

= 14 < 15

(b) 1 : 7 and 5 :  2

= 2 < 25

(c) 5 : 8 and 7 :  5

= 5/8 < 7/5

= 25 < 56

5 : 8 and 7 : 5

(d) 12 : 5 and 7 : 3

= 12/5 > 7/3

= 36 : 35

= 12 : 5 > 7 : 3

Question no – (18)

Solution :

Let, Sana gets = 1

Priya gets = 2

Ram gets (4 × 2) = 8

Ram gets shall,

= (220 × 8/11)

= 160

Priya gets shall,

= (220 × 2/11)m

= 40

Sana gets shall

= (220 × 1/11)

= 20

Ratio and Proportion Exercise 7.2 Solution :

Question no – (1)

Solution :

(a) 12, 16, 21, 28

Product of means

= (16 × 21) = 336

and, Product of extremes

= (12 × 28) = 336

This is in proportion

(b) 21, 16, 25, 20

Product of extremes

= (20 × 21) = 420

and, Product of measures of means

= (16 × 25) = 400

This is not I proportion

(c) 1, 5, 5, 25

Product of extremes

= (25 × 1) = 25

This is in proportion

(d) 23, 44, 75, 100

Product of extremes

= (100 × 23) = 2300

Product of means

= (44 × 75) = 3300

This is not in proportion

(e) 4, 9, 12, 27

Product of extremes = (27 × 4) = 108

Product of means = (9 × 12) = 108

This is in proportion

Question no – (2)

Solution :

(a) Statement is – True

(b) Statement is – False

(c) Statement is – True

(d) Statement is – False

(e) Statement is – False

(f) Statement is – False

Question no – (3)

Solution :

(a) 12 : 20 : : 96 : x

= 12/20 = 96/x

= x = 20 × 96/12

= 160

(b) 2, 9, x, 72

= 2 : 9 : : x : 72

= 2/9 = x/12

= x = 72 × 2/9

= 16

(c) 4, x, 24, 42

= 4 : x : : 24 : 42

= 4/x = 24/42

= x = 4 × 42/24

= 7

(d) x : 14 : 15 : : 30

= x/14 = 15/30

= x = 14 × 15/30

= 7

(e) x, 30, 24, 16

x : 30 : : 24 : 16

= x/30 = 24/16

= x = 30 × 24/16

= 45

(f) 12, 18, 14, x

= 12 : 18 : : 14 : x

= 12/18 = 14/x

= x = 18 × 14/12

= 21

Question Number – 4

Solution :

(a) Yes it formed d

Middle terns = 2m 8.50 Rs

Extreme terms

= 25 cm and 400 Rs

(b) Yes, here, middle terms 50 Kg, 150 gm

Extremes terms,

= 3 kg, 25 kg

(c) Yes, if forms Middle terms 50 is 200 ml

Extremes forms

= 4 Rs and 2.5

(d) Do it is not

Question no – (5)

Solution :

= 20 people required 3 kg rice

= 1 people required 3/20 kg rice

50 people required 50 × 3/20

= 15/2

= 7.5 kg

Question no – (6)

Solution :

Grocery : Education = 2 : 5

Therefore 2 – 980 s

= 1 – 980/2 Rs

5 – 980 × 5/2

= (490 × 5) Rs

= 2450 Rs

Question no – (7)

Solution :

Ram : Rahim = 4 : 7

7 unit – 21 years

1 unit – 21/7 years

4 unit – 21 × 4/7

= 12 years

Question no – (8)

Solution :

= 8 km distance cover in 10 min

1 km distance cover in 10/8 min

36 km distance cover in 10 × 36/8

= 45 min

Question no – (9)

Solution :

General books : textbooks = 3 : 1

Total = (3 + 1) = 4

3 – 1800

= 1 – 1800/3

4 – 1800 × 4/3

= 2400 books

Question no – (10)

Solution :

Income : Expenditure,

= 7 : 6

Saving

= (7 – 6) = 1

Income,

= 7 – 9100

= 1 – 9100/7

1 – 1300 Rs

Question no – (11)

Solution :

1st : 2nd = 7 : 9 (speed)

630 km cover in 14 h

Speed = 630/14

= 45 km/h

9 unit – 45

= 1 unit – 45/9

7 – 45 × 7/9

= 35

Time = 630/35

= 18 h

Question no – (12)

Solution :

Ratio = 2 : 7

Total = (2 + 7) = 9

= 2 – 400 books

1 – 400/2

9 – 400 × 9/2

= 1800 books

Question no – (13)

Solution :

Length : width,

= 5 : 3

3 unit – 36 m

1 unit – 36/3 m

5 unit – 36 × 5/3

= 60 m

Question no – (14)

Solution :

Income : Expenditure

= 8 : 7

= 7 unit – 12,6000

= 1 unit – 126000/7

= 18000 Rs

8 unit – (18000 × 8)

= 144000 Rs

Monthly income,

= 144000/12 Rs

= 12000 Rs

Question no – (15)

Solution :

Length: breadth = 4 : 3

∴ 4 – 60 cm

= 1 – 40/4 cm

∴ 3 – 60 × 3/4

= 45 cm

Question no – (17)

Solution :

= 8 cm high contain 488 ml

1 cm high contain 488/8 ml

15 cm high contain (488/8 × 15) ml

= 61 × 15

= 915 ml

Question no – (18)

Solution :

Let, 4th tower x

= 15 : 20 : : 30 : x

= 15/20

= 30/x

= x = 20 × 30/15

= 40

Question no – (19)

Solution :

Let, 2nd term x

42 : x : : 70 : 35

= 42/x

= 70/35

= x = 35 × 42/70

= 21

Question no – (20)

Solution :

Let, 1st term x

x : 5 : : 15 : 25

= x/5 = 15/25

= X = 5 × 15/25

= 3

1st term is 3

Ratio and Proportion Exercise 7.3 Solution :

Question no – (1)

Solution :

= 12 eggs cost 36 Rs

1 eggs cost 36/12 Rs

7 eggs cost

= 36 × 7/12

= 21 Rs

Question no – (2)

Solution :

Price of 18 kg rice is,

= 549 Rs

Price of 1 kg rice

= 549/8 Rs

Price of 22 kg rice is,

= 549 × 22/18

= 671

Question no – (3)

Solution :

In 65 rows terms have

= 2275

In 1 rows terms have

= 2275/65

In 20 rows terms have

= 2275 × 20/65

= 700 terms

Question no – (4)

Solution :

= Bus 36 km cover I 40 min

Bus 1 km cover in 40/36 min

Bus 162 km cover in 40 × 162/36

= 180 min

= 3 h

Now, In bus cover 162 km

1 h bus cover 162/3 min

8 h bus cover 162 × 8/3 km

= 54 × 8

= 432 km

Question no – (5)

Solution :

= 10 high pole casts a shadow of 6 m

1 m high pole costs  shadow of 6/10 m

6 m high pole costs a shadow 6 × 6/10 m

= 36/10

= 3 : 6 m

Question no – (6)

Solution :

= Ratio journey 75 km cost 315 Rs

Ratio journey 1 km cost 315/7 Rs

Ratio journey 120 km cost

= 315 × 120/75

= 504 Rs

Question no – (7)

Solution :

In 5 hour cover 250 km

In 1 hour cover 250/5 km

9 hour cover 250 × 9/5 km

= 450 km

Question no – (8)

Solution :

= 15 packets of 12 pencil cost 288 Rs

1 packets of 12 pencil cost

= 288/15 × 12

20 packets 10 pencil cost

= 288 × 20 10/15 × 12

= 320 Rs

Question no – (9)

Solution :

= 8 h a day takes 6 days

= (8 × 6)

= 48 total

Now, to complete 16 days

= 48/16

= 3h/day

Question no – (10)

Solution :

= 22 bags of wheat 20 kg cost 3520 Rs

22 bags of wheat weighing 20 kg cost

= 3520/22 × 20

15 boys of wheat weighing 8 kg cost

= 3524 × 25 × 8/22 × 20

= 960 Rs

Ratio and Proportion Exercise 7.4 Solution :

Question no – (1)

Solution :

(a) S = 90 km/hour

(b) S = 70 km/hour

(c) S = 12 m/s

(d) S = 90 m/s

Question no – (2)

Solution :

(a) 120 km

(b) 120 km

(c) 200 m

(d) 1000 m

Question no – (3)

Solution :

(a) 11 hour

(b) 40 hour

(c) 40 s

(d) 60 s

Question no – (4)

Solution :

(a) (45 × 18/5) km/h

= 162 km/hour

(b) 60 m/s

= (60 × 18/5) km/h

= 216 km/hour

(c) 90 m/s

= (90 × 18/5) km/h

= 324 km/hour

(d) 100 m/s

= (100 × 18/5) km/h

= 360 km/hour

Question no -(5)

Solution :

(a) 90 km/L

= (90 × 5/18) m/s

= 25 m/s

(b) 108 km/h

= (108 × 5/18) m/s

= 30 m/s

(c) 144 km/h

= (144 × 5/18) m/s

= 40 m/s

(d) 198 km/h

= (198 × 5/18) m/s

= 55 m/s

Question no – (6)

Solution :

Truck, 1 hour cover 72 km

8 hour cover (72 × 8) km

= 576 km

Question no – (7)

Solution :

Speed,

= 900/12

= 75 km/hour

Question no – (8)

Solution :

= 1s travel 30 m

4 1/2 s travel

= (30 × 4 1/2) m

= 30 × 2/9

= 135 m

Question no – (9)

Solution :

= 1 h travelled 16 km

5 h travel

= (16 × 5) km

= 80 km

Question no – (10)

Solution :

Spaceship 3 h travels 45000 km

Speed = 45000/3

= 15000 km

Question no – (11)

Solution :

Speed,

= 18000/2 km/h

= 9000 km/hour

Question no – (12)

Solution :

= 180 km/h

= (180 × 5/18) m/s

= 50 m/s

1s ball travel 50 m

Question no – (13)

Solution :

Speed = 960/16 km/h

= 60 km/h

Next Chapter Solution :

Updated: June 23, 2023 — 6:45 am