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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
(c) Female : made
= 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
= 1/7 ad 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
breadth 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 :
👉 Chapter 8 👈