Collins Maths Solutions Class 6 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 Collins Maths Class 6 Mathematics, Chapter 7, Ratio and Proportion. Here students can easily find Exercise wise solution for chapter 7, Ratio and Proportion. Students will find proper solutions for Exercise 7.1 Our teacher’s solved every problem with easily understandable methods so that every students can understand easily. Here in this post all the solutions are based on ICSE latest Syllabus.
Ratio and Proportion Exercise 7.7 Solution :
Question no – (1)
Solution :
(a) 24 : 72
= 24/72
= 1/3
= 1 : 3 ….(simplest from)
(b) 80 : 112
= 80/112
= 5/7
= 5 : 7 ….(simplest from)
(c) 130 : 160
= 130/160
= 13/16
= 13 : 16 ….(simplest from)
(d) 629 : 407
= 629/407
= 629 : 407 ….(simplest from)
Question no – (2)
Solution :
(a) Rs 7, Rs 1.75
Ask we know,
1 rupee = 100 paise
∴ Rs 1.75 = 100 + 75 = 175 paise
Now,
= 700 : 175
= 140 : 35
= 28 : 7
= 4 : 1 …..(simplest form)
(b) 5 m, 150 cm
As we know,
1 m = 100 cm
∴ 5 m = 500 cm
Now, = 500 : 150
= 50 : 15
= 10 : 3 …..(simplest form)
(c) 6 h, 1 h 50 min
As we know that, 1 hour = 600 minute
Now,= 6h = 6 × 60 min [1 hour 60 min]
= 360 min
= 1 h 50 min = 1 × 60 + 50 min
= 60 + 50 min
= 110 min
= 360 : 110
= 36 : 11 …..(simplest form)
(d) 6 l, 625 ml
As we know, 1 litre = 1000 ml
∴ 6l = 6 × 100 ml = 6000 ml
= 625 ml
Now, = 600 : 625
= 1200 : 125
= 240 : 25
= 48 : 5 …..(simplest form)
Question no – (3)
Solution :
(a) 1 : 6/7
= 1 × 7 : 6/7 × 7
= 7 : 6
(b) 7/12 : 2
= 17/12 × 12 : 2 × 12
= 7 : 24
(c) 3/4 : 5/6
= 3/4 × 4 × 6 : 5/6 × 6 × 4
= 18 : 20
(d) 5 1/2 : 3 2/3
= 5 × 2 + 1/2 : 3 × 3 × 2/3
= 12/2 : 11/3
= 11/2 × 2 × 3 : 11/3 × 3 × 2
= 33 : 22
= 3 : 2
Question no – (4)
Solution :
(a) Given, 3 : 5, 27 : 45
= 3 : 5 = 3/5
= 27/45 = 3/5
∴ Education is equivalent
(b) Given, 2 : 3, 30 : 20
= 2 : 3 = 2/3
= 30 : 20 = 30/20
= 3/2
∴ This equitation is not equivalent
(c) Given, 7 : 4, 126 : 64
= 7 : 4 = 7/4
= 126 : 64 = 63/32
∴ This equation is not equivalent.
(d) Given, 21 : 50, 43 : 100
= 135 : 30 = 135/30
= 9/2
= 9 : 2 = 9/2
∴ This equation is equivalent.
Question no – (5)
Solution :
(a) Given ratios, 5 : 6, and 6 : 7
= 5 : 6 can be written as = 5/6
= 6 : 7 can be written as = 6/7
LCM of the denominator 6 and 7 is 42
Now, making the denominator of each fraction equal to 42
= 5 × 7/6 × 7 = 35/42,
= 6 × 6/7 × 6 = 36/42
∴ 35/42 < 36/42
(b) Given ratios are 19 : 25 and 37 : 50
= 19 : 25 can be written as 19/25
= 37 : 50 can be written as = 37/50
LCM of 25 and 50 is 50
Now, making the denominator of each fraction equal to 50
= 19 × 2/25 × 2 = 38/50,
= 37 × 1/50 × 1 = 37/50
∴ 38/50 > 37/50
(c) Given ratios are, 24 : 13 and 12 : 7
= 7 : 4 can be written as 7/4
= 126 : 64 can be written as 126/64
LCM of 4 and 8 is 8
Now, making the denominator of each fraction to 8
= 7 × 2/4 × 2 = 14/8,
= 63 × 1/8 × 1 = 63/8
∴ 14/8 < 63/8
(d) Given ratios are, 21 : 50, 43 : 100
= 135 : 30 = 135/30
= 43 : 100 = 9 : 2 = 9/2
LCM of 2 and 30 is 30
Now, making the denominator of each fraction to 30
= 135 × 1/30 × 1 = 135/30
= 9 × 15/2 × 15 = 135/30
∴ 135/30 = 135/30
∴ 21 : 50 = 43 : 100
Question no – (6)
Solution :
(a) 2, 3, 22, 33
= In the given numbers,
Product of extremes = 2 × 33 = 66
Product of means = 3 × 22 = 66
∴ Product of extremes = product of means
∴ Therefore 2, 3, 22, 33 are in proportion
(b) 8, 6, 12, 9
= In the given number
Product extremes = 8 × 9 = 72
Product of means = 6 × 12 = 72
∴ product of extremes = product of money
∴ Therefore 8, 6, 12, 9 are in proportion.
(c) Given, 15, 30, 7, 14
= In the given number,
product extremes = 15 × 14 = 210
Product of means = 30 × 7 = 210
Product of extremes = product of means
∴ Therefore 15, 30, 7, 14, are in proportion
(d) 15, 21, 25, 40
In the given number
Product of extremes = 15 × 40 = 600
Product of means = 21 × 25 = 525
Product of extremes ≠ product of means
Therefore 15, 21, 25, 40 are not in proportion.
Question no – (7)
Solution :
(a) 24 : 18 = 12 : 9
(b) 12 : 16 = 9 : 12
= 16 × 9 = 144
= 144/12 = 12
(c) ____ : 20 = 5 : 2 1/2
= 50 : 5/2
= 5 × 2 : 5/2 × 2
= 40 : 20 = 10 : 5
(d) 10 1/2 : ____ = 5 1/2 : 2 3/4
= 21/2 : ____ = 11/2 : 11/4
= 11/2 × x = 1/4 × 21/2
= 11x/2 = 11 × 21/8
= x = 11 × 21 × 2/8 × 11
= x = 21/4
= x = 5 1/4
∴ 21/2 : 5 1/4 = 11/4 × 21/2
Question no – (8)
Solution :
(a) Let, the fourth proportion is x
∵ Product of extremes = Production of money
= 16 × x = 12 × 4
= x = 12 × 4/16
= x = 3
∴ Fourth proportion will be 3
(b) Let, the fourth proportion is x
∵ Product of extremes = product of means
= 9 × x = 10 × 18
= x = 10 × 18/9
= x = 20
Therefore, fourth proportion will be 20
(c) Let, the fourth proportion is x
∵ Product of extremes = Production of money
= 10 × x = 20 × 15
= x = 20 × 15/10
= x = 30
Hence, fourth proportion will be 30
(d) Let, the fourth proportion is = x
∵ Product of extremes = Production of money
= 24 × x = 18 × 12
= x = 18 × 12/24
= x = 9
Thus, fourth proportion will be 9
Question no – (9)
Solution :
As per the given question,
250 ml of mango squash requires 2 of water.
∴ Ratio of waterer and mango squash,
= (2 × 1000 ml) : 250 ml
= 200 : 250
= 200 : 25
= 8 : 1
Therefore, the ratio of water to mango squash will be 8 : 1
Question no – (10)
Solution :
First, Length of one part,
= 114 cm × 9/19
= 54 cm
Now, Length of another part,
= 11 ×10/19
= 60 cm
Therefore, the length of the two parts will be 54 cm and 60 cm.
Question no – (11)
Solution :
Water in total mixture,
= 2/5 + 2
= 2/7
Fraction of milk in total mixture,
= 5/5 + 2
= 5/7
∴ On 6.3 milk water mixed by him,
= 6.3 × 2/7
= 63/10 × 2/7
= 18/10
= 1.8L
Therefore, the milkman will mixed 18 liter of water in 6.3 liter milk.
Question no – (12)
Solution :
According to the question,
The ratio of three angles in a triangle is = 1 : 2 : 3
∴ The fraction of three angle are,
= 1/1 + 2 + 3 = 1/6,
= 2/12 + 3 = 2/6,
= 3/1 + 2 + 3 = 3/6
∴ 180 × 1/6 = 30°
∴ 180 × 2/6 = 60°
∴ 180 × 3/6 = 90°
∴ The angles are 30°, 60°, 90°
Question no – (13)
Solution :
(i) the number of girls and boys.
= The number of boys is = 16
The number of girls is,
= (30 – 16)
= 14
∴ Ratio of boys and girls,
= 16 : 14
= 8 : 7
Ratio of boys and girls,
= 16 : 14
= 8 : 7
Ratio of girls and boys,
= 7 : 8
(ii) the number of girls and the whole class.
= The number of girls and the whole class,
= 14 : 30
= 7 : 15
Question no – (14)
Solution :
It is saving,
= (500 – 2000)
= 200
(i) His saving,
Ratio of expenditure and saving
= 3000 : 2000
= 3 : 2
Hence, the ratio of his expenditure to saving will be 3 : 2
(ii) His total income,
= Ratio of expenditure and total income
= 3000 : 5000
= 3 : 5
Therefore, the ratio of his expenditure to total income will be 3 : 5
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