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Brilliant’s Composite Mathematics Class 6 Solutions Chapter 8 Unitary Method Ratio and Proportion
Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of Brilliant’s Composite Mathematics Class 6 Math Book, Chapter 8, Unitary Method Ratio and Proportion. Here students can easily find step by step solutions of all the problems for Unitary Method Ratio and Proportion, Exercise 8.1, 8.2 and 8.3 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily.
Unitary Method Ratio and Proportion Exercise 8.1 Solution
Question no – (1)
Solution :
According to the question,
15 litres of milk cost Rs 165,
The cost of 9 litres of milk = ?
∴ Cost of 1 litres milk,
= 165/15
= 11 Rs.
∴ Cost of 9 litres milk,
= 11 × 9
= 99 Rs.
Thus, the cost of 9 litres of milk will be Rs. 99
Question no – (2)
Solution :
As per the given question,
7 packets of sugar weigh = 21 kg,
The weight of 11 such packets of sugar = ?
∴ Weight of 1 packets sugar,
= 213/7
= 3 kg
∴ Weight of 11 packets sugar,
= 3 × 11
= 33 kg
Hence, the weight of 11 such packets of sugar will be 33 kg.
Question no – (3)
Solution :
According to the question,
9 soap-cakes cost = Rs 31.5,
The cost of one dozen such soap-cakes = ?
We know, One dozen = 12 piece
∴ Cost of 1 soap-cakes,
= 31.5/90
= 35/10
∴ Cost of 12 soap-cakes,
= 35/10 × 12
= 42 Rs.
Therefore, the cost of one dozen such soap-cakes will be Rs. 42
Question no – (4)
Solution :
As per the given question,
The cost of 8 kg of rice is = Rs 284,
The cost of 50 kg rice = ?
∴ Cost of 1 kg of rice is,
= 284/8
= 71/2
∴ Cost of 50 kg of rice is,
= 71/2 × 50
= 1775 Rs.
Therefore, the cost of 50 kg of such quality of rice will be Rs. 1775
Question no – (5)
Solution :
According to the question,
71 kg 500 gms of fodder is sufficient to feed = 11 cows,
123 kg 500 gms of fodder is sufficient to feed = ? cows
∴ 1 kg fodder for,
= 11/71.5
∴ 123.5 kg fodder for,
= 11 × 123/71.5
= 19 cows
Hence, 123 kg 500 gms of fodder is sufficient to feed 19 cows.
Question no – (6)
Solution :
As per the question we know,
The weight of 45 folding chairs is = 18 kg.
Truck having a capacity of 4000 kg load = how many chairs?
∴ 1 kg weight for folding chairs,
= 45/18
∴ 4000 kg weight for folding chairs,
= 45 × 4000/18
= 10000 chairs.
Thus, 10000 chairs can be loaded on the truck.
Question no – (7)
Solution :
According to the question,
The yield of wheat from 6 hectares is = 280 quintals.
The number of hectares required for a yield of 225 quintals = ?
∴ Wheat from 1 quintals is,
= 6/280 hectors
∴ Wheat from 225 quintals is,
= 6 × 225/280
= 135/28
= 4 23/28 hectares.
Thus, the number of hectares required for a yield of 225 quintals is 4 23/28 hectares.
Question no – (8)
Solution :
According to the question,
Fifteen inlands cost = Rs 22.50.
The cost of 36 inlands = ?
Inlands can we buy for Rs 67.5 =?
∴ 15 inlands cost is,
= 22.50/150
= 15/10
∴ 36 inlands cost is,
= 15/10 × 36
= 54
Now, 22.50 is the cost of 15 inlands
∴ 1 is the cost is,
= 150/22.50
= 10/15
∴ 67.5 is the cost is,
= 10/15 × 67.5/10
= 45 inlands
Therefore, we can buy 45 inland.
Question no – (9)
Solution :
According to the question,
The price of 5 metres of cloth is = Rs 132.5.
The price of 17 metres of cloth = ?
∴ Price of 1 meters of cloth is,
= 132.5/5
∴ Price of 17 meters of cloth is,
= 132.5 × 17/5 × 10
= 4505/10
= 450.5 Rs.
Therefore, the price of 17 metres of cloth will be Rs.450.5
Question no – (10)
Solution :
As per the question we know,
12 leaves of bread each weighing 400 gm cost = Rs 48.
The cost of 26 leaves of bread if each weigh 500 gms = ?
Now,
12 leaves of bread each weighing 400 gm cost = 48
1 leaves of bread each weighing 1 gm cost = 48/12 ×400
∴ 26 leaves of bread each weighing 500 gm cost,
= 48/12 × 400 × 500 × 26
= 130 Rs.
Therefore, the cost of 26 leaves bread will be 130 Rs.
Question no – (11)
Solution :
(i) The bus travels 324 km in 8 hours,
The bus travels 243 km in
= 8/324 × 243
= 6 hours
(ii) The bus takes 8 hours for travels 324 km,
The bus takes 1 hours for travels 324/8 km
The bus takes 13/2 hours for travels,
= 324/8 × 13/2
= 1053/4
= 263.25 km
Question no – (12)
Solution :
According to the question,
52 packets containing 1 dozen pencil each cost = Rs 499.20.
The cost of 85 packets of 10 pencils each = ?
Now,
Cost of 52 packets containing 12 pencil is = 499.20
∴ Cost of 1 packets containing 1 pencil is,
= 499.20/52 × 12
∴ Cost 85 packets containing 10 pencil is,
= 499.20/52 × 12 × 10 × 85 × 10
= 8 × 89
= 680 Rs.
Thus, the cost of 85 packets of 10 pencils each will be Rs. 680
Question no – (13)
Solution :
As per the question we know,
A map uses 3 cm to represent 36 km.
The distance between two cities on a map is 48 cm,
Now, Map uses 3 cm to represent = 36 km
∴ Map uses 1 cm to represent = 36/3 km
∴ Map uses 48 cm to represent,
= 36 × 48/3
= 576 km
Therefore, the cities are 576 km kilometres apart.
Question no – (14)
Solution :
According to the given question we know,
The cost of 25 chairs is Rs 8125
Chairs can be purchased for Rs 5525 = ?
Now,
8125 is cost of = 25 chairs
∴ 8125 is cost of
= 26/8125 chairs
∴ 5525 is cost of,
= 25 × 5525/8125
= 17 chairs
Therefore, 17 chairs can be purchased for Rs 5525.
Question no – (15)
Solution :
As per the question we know,
7.5 gm of an alloy of copper and zinc contains 4.5 gm of zinc
Weight of zinc will be these in 25 gm of the alloy = ?
Now, 7.5 gm of an alloy contains = 4.5 gm of zinc
∴ 1 gm of an alloy contains,
= 4.5/7.5 gm of zinc
∴ 25 gm of an alloy contains,
= 45 × 25/75 gm of zinc
= 15 gm of zinc
Therefore, the weight of the zinc will be 15 gm.
Unitary Method Ratio and Proportion Exercise 8.2 Solution
Question no – (1)
Solution :
(i) The number of females in a village is three times the number of males
As ratio :
Number of females = 1/3 number of males
∴ number of females/number of males = 1/3
∴ Number of females : number of males = 1 : 3
∴ The ratio is = 1 : 3
(ii) The number of students passing English test in a class is three-fourth of the number that appeared.
Now as ratio :
= Number of students passing English test/number that appeared = 3/4
∴ The ratio is = 3 : 4
(iii) The number of girls working in an office is two-thirds of the number of boys.
Now as ratio.
= Number of girls/number of boys = 2/3
∴ The ratio is = 2 : 3
(iv) The speed of a car is twice the speed of a scooter
Now as ratio,
= Speed of car/speed of scooter = 2/1
∴ The ratio is = 2 : 1
Question no – (2)
Solution :
(i) 200 to 850
It can be written as 200 : 850
∴ 200 : 850
= 200/850
= 4/17
= 4 : 17
Therefore, 4 : 17 is the simplest form of 200 to 850.
(ii) 95 to 380
It can be written as 95 : 380
∴ 95 : 380
= 95/380
= 1/4
= 1 : 4
Therefore, 1 : 4 is the simplest form of 95 to 380.
(iii) 18 to 81
It can be written as 18 to 81
∴ 18 : 81
= 18/81
= 6/27
= 6 : 27
Therefore, 6 : 27 is the simplest form of 18 to 81.
(iv) 50 paise to Rs 4
It can be written as 50 : 400
∴ 50 : 400
= 50/400
= 1/8
= 1 : 8
Therefore, 1 : 8 is the simplest form of 50 paise to Rs 4.
(v) 150 g to 3 kg
It can be written as 150 : 3000 (∵ 1 kg = 1000 gm)
∴ 150 : 3000
= 150/3000
= 1/20
= 1 : 20
Therefore, 1 : 20 is the simplest form of 150 g to 3 kg.
(vi) 56 minutes to 1 hour
It can be written as 56 : 60 (∵ 1 hour = 60 min)
∴ 56 : 60
= 56/60
= 14 : 15
Therefore, 14 : 15 is the simplest form of 56 minutes to 1 hour.
(vii) 40 seconds to 50 minutes
It can be written as 56 min : 1h
∴ 56 min : 1 h
= 56 : 60
= 56/60
= 14 : 15
Therefore, 14 : 15 is the simplest form of 40 seconds to 50 minutes.
(viii) two dozen to a score
It can be written as 24 : 20
∵ Two dozen = 24 and a score = 20
∴ 24 : 20
= 6 : 5
= 24/20
Therefore, 6 : 5 is the simplest form of two dozen to a score.
(ix) 35 cm to 50 mm
It can be written as 35000 : 50
∵ 1 mm = 104 cm
∵ 35 cm = 35 × 104 = 35000 mm
∴ 35000 : 50
= 35000/50
= 700 : 1
Therefore, 700 : 1 is the simplest form of 35 cm to 50 mm.
(x) 45 cm to 3 metres
It can be written as 45 cm : 3 m
∴ 45 cm : 3 m
= 45 cm : 300 cm
= 45/300
= 3 : 20
Therefore, 3 : 20 is the simplest form of 45 cm to 3 metres.
(xi) 3.2 metres to 56 metres
It can be written as 3.2 : 56
∴ 3.2 : 56
= 32/560
= 2/35
= 2 : 35
Therefore, 2 : 35 is the simplest form of 3.2 metres to 56 metres.
(xii) 10 litres to 0.25 litre
It can be written as 10 : 0.25
∴ 10 : 0.25
= 10 × 100/0.25
= 40/1
= 40 : 1
Therefore, 40 : 1 is the simplest form of 10 litres to 0.25 litre.
(xiii) Rs 6.30 to Rs 16.80
It can be written as 6.30 : 16.80
∴ 6.30 : 16.80
= 6.30/16.80
= 630/1680
= 3/8
= 3 : 8
Therefore,3 : 8 is the simplest form of Rs 6.30 to Rs 16.80.
(xiv) 25 paise to Rs 6
It can be written as 25 paise : 6
∴ 25 paise : 6
= 25 : 600
= 25/600
= 1/24
= 1 : 24
Therefore, 1 : 24 is the simplest form of 25 paise to Rs 6.
(xv) 200 kg to a quintal
It can be written as 200kg : 100kg
∴ a quintal = 100 kg
= 200kg : 100kg
= 200/100
= 2/1
= 2 : 1
Therefore, 2 : 1 is the simplest form of 200 kg to a quintal.
(xvi) 2.5 quintal to a ton
It can be written as 2.5 quintal : a ton
∴ 2.5 quintal : a ton
= 2.5 : 10
= 2.5/100
= 1/4
= 1.4
Therefore, 4 : 17 is the simplest form of 2.5 quintal to a ton.
Question no – (3)
Solution :
(i) Amit’s income to Sumeet’s income,
= Amit : Sumeet = 5400 : 9750
= 5400/9750
= 36:65
(ii) Amit’s income to their total income,
Total income,
= (5400 + 9750)
= 15150
∴ Amit : total = 54 : 15150
= 5400/15150
= 36 : 101
Question no – (4)
Solution :
According to the question,
Ram has a total income of Rs 1850 per month.
Ram spends Rs 1375 on his family
(i) Ram’s expenditure to his income,
Income = 1850
Expenditure = 1375
∴ 1375 : 1850
= 1375/1850
= 55 : 74
(ii) Ram’s savings to his expenditure,
Saving = 1850 – 1375 = 475
∴ 475 : 1375
= 475/1375
= 19 : 55
(iii) Ram’s savings to his income,
Saving : income = 475 : 1850
= 475/1850
= 19 : 74
Question no – (5)
Solution :
According to question we know,
Car travels 72 km is 1.30 hours
Train travels 130 km in 2 hours.
The ratio of their speeds = ?
Car Cover Distance = 72km
Time = 1.30 h
∴ Speed = 720/1.3
= 720/13
Train Cover Distance = 130km
Time = 2h
∴ Speed = 130/2
∴ Ratio of their speeds,
= 720/13 : 130/2
= 720/13 × 2/130
= 144/169
= 144 : 169
Hence, the ratio of their speeds will be 144 : 169
Question no – (6)
Solution :
(i) His savings to his income,
Income = 1755
Saving = 395
∴ 395 : 1755
= 395/1755
= 79:351
(ii) His income to his expenditure,
Expenditure = 1755 – 395
= 1360
(iii) His expenditure to his savings,
= Expenditure : savings
= 1360 : 395
= 1360/395
= 272 : 79
Question no – (7)
Solution :
(i) Men to that of women,
Men = 105
Women = (195 – 105) = 90
∴ 105 : 90
= 105/90
= 7 : 6
(ii) Women to the total number of persons,
Total = 195
∴ 90 : 195
= 90/195
= 6 : 13
(iii) Men to total number of persons,
Men : Total persons
= 105 : 195
= 105/195
= 7 : 13
Question no – (8)
Solution :
(a) Income tax to her Income,
Income = 64000
Income tax = 15000
∴ 15000 : 64000
= 15000/64000
= 15 : 65
(b) her Income to Income tax,
= 64000 : 15000
= 64000/15000
= 64 : 15
(c) Are the two ratio same?
= No the two ratio are not same.
Question no – (9)
Solution :
Time period of the office,
= 8.30 am to 5 pm
= 8.30 hour
= 510 min
(i) Including lunch interval,
= 45 : 510
= 45/510
= 3 : 34
(ii) Excluding lunch interval,
= 45 : (510 – 45)
= 45 : 465
= 45/465
= 3 : 31
Question no – (10)
Solution :
In the given question,
The length of a measuring tape is = 9 m
The width of a measuring tape is = 3.5 cm
9 m = 900 cm …(∵ 1 m = 100 cm)
∴ 900 : 3.5
= 9000/3.5
= 1800 : 7
Question no – (11)
Solution :
From the question we get,
7 km = 7000 m
2.5 hours = 150 min
∴ A’s speed,
= 7000/150
= 700/15
∴ B’s speed,
= 250/5
∴ A/B
= 700/15 × 5/250
A/B = 14/15
= A : B = 14 : 15
Hence, the ratio of their speeds will be 14 : 15
Question no – (12)
Solution :
(i) 3 : 5 or 2 : 3
Now, 3/5 = 3×3/5×3 = 9/15
2/3 = 2 × 5/3 × 5 = 10/15
∴ 10/15 > 9/15
= 2/3 > 3/5
Thus, 2 : 3 is greater.
(ii) 4 : 9 or 7 : 15
Now, 4/9 = 4 × 5/9 × 5 = 20/45
7/15 = 7×3/15×3 = 25/45
∴ 7/15 > 4/9
Thus, 7 : 15 is greater.
(iii) 3 : 7 or 8 : 12
Now, 3/7 = 3 × 12/7 × 12 = 36/84
8/12 = 8 × 72/12 × 7 = 56/84
∴ 8/12 > 3/7
Thus, 8 : 12 is greater.
(iv) 0.5 : 15 or 0.25 : 1
Now, 0.5/150 = 1/30 = 1 × 2/30 × 2 = 2/60
0.25/100 = 1/4 = 1 × 15 /4×15 = 15/60
∴ 0.25/1 > 0.5/15
(v) 47 : 60 or 91 : 108
Now, 47/60 = 47 ×9/60 × 9 = 423/540
91/108 = 91×5/108×5 = 455/540
∴ 91 : 108 > 67 : 60
(vi) 3 : 4 or 5 : 6
Now, 3/4 = 3×3/4× = 9/12
5/6 = 5×2/6×2 = 10/12
∴ 5 : 6 > 3 : 4
(vii) 2 : 3 or 18 : 36
Now, 3/5 = 3×3/5×3 = 9/15
2/3 = 2 × 5/3 × 5 = 10/15
∴ 10/15 > 9/15
∴ 2/3 > 3/5
Question no – (14)
Solution :
According to the question,
A shopkeeper earns Rs. 5265 monthly and spends Rs. 2340
Now,
Income : Expenditure
= 5265 : 2340
= 5265/2340
= 1053 : 468
Hence, the ratio between his income and expenditure will be 1053 : 468
Question no – (15)
Solution :
According to the question,
The ratio of alcohol to water in a solution is 3 to 6,
Another solution the ratio of ammonia to water is 3 to 5
Now,
3/6 = 3 × 5/6 × 5 = 15/30
3/5 = 3 × 6/5 × 6 = 18/30
Therefore, ammonia to water is “Greater”
Question no – (16)
Solution :
Cost of 1 kg of coffee,
= 24/100 × 1000
= 240
Required ratio of and tea,
= 240 : 80
= 3 : 1
∴ The ratio of price of the coffee to that tea will be 3 : 1
Question no – (17)
Solution :
Cost of 1 ball pen = 54/12
Cost of 1 pencil = 16/20
∴ Pen : Pencil
= 54/12 : 16/20
= 54/12 × 20/16
= 45/8
= 45 : 8
Thus, the ratio of the price of a ball pen to a pencil will be 45 : 8
Unitary Method Ratio and Proportion Exercise 8.3 Solution
Question no – (1)
Solution :
Product of extremes = product of means
(i) Given, 8 : 12 = 20 : 30
= 8 × 30 = 420
and 12× 20 = 240
∴ True.
(ii) 14 : 28 = 15 : 30
= 14 ×30 = 420
and 28 ×15= 420
∴ True.
(iii) 18 : 12 = 24 : 36
= 18 : 12 = 24:36
18/ 12 = 24/36
3:1 = 4:3
3 ×3 = 9
4 ×1 = 4
∴ not true.
(iv) 25 m : 50 m = 4 cm =: 8 cm
= 25m : 50m = 4cm: 8cm
= 2500 : 5000 = 4:8
= 2500/5000 = 4/8
= 1 : 2 = 1:2
∴ 1×2 = 2 and 1×2 = 2
∴ True.
(v) 25 men : 75 men = Rs 125 : Rs 375
= 25/75 = 125/37
1/3 = 1/3
1:3 = 1:3
1× 3 = 3 and 1×3 = 3
∴ True.
(vi) 70 kg : 35 kg = 30 gm : 70 gm
= 70 kg : 35 kg = 30 gm : 70 gm
= 70000/25000 – 30/70
= 2 : 1 = 3 :7
∴ 2 × 7 = 14 and 1 × 3 = 3
∴ It is not true.
Question no – (2)
Solution :
(i) 8, 6, 20, 15
8 × 15 = 120
and 6 × 20 = 120
∴ proportion
(ii) 5, 9, 1, 5, 37
= 15 × 37 = 185
and 9 ×15 = 135
∴ not proportion
(iii) 7, 5, 14, 12
7 × 12 = 84
and 5 × 14 = 70
∴ not proportion
(iv) 10, 18, 25, 45
10 ×45 = 450
and 5 ×14 = 70
(v) 4, 19, 9, 14
4 × 14 = 56
and 19 x 9 = 171
∴ not proportion
(vi) 35, 45, 45, 39
35 × 39 = 1365
and 45 × 45 = 2025
∴ not proportion
Question no – (8)
Solution :
(i) Let the mean proportion be x
Now, x^2 = 49 × 25
x = √7 × 7 × 25 × 5
= 7 × 5
= 35
Hence, the mean proportion between 49 and 25 is 35
(ii) Given number = 16 and 121
Let the mean proportion be x
Now, x = √16 × 121
= 4 ×11
= 44
Hence, the mean proportion between 16 and 121 is 44
(iii) Let the mean proportion be x
Now, x = √32 × 338
= √16 × 2 × 2 × 169
= 2 × 4 × 13
= 104
Thus, the mean proportion between 32 and 338 is 104
Question no – (9)
Solution :
x^2 = 4 × 81 ….(according to the question)
x = √4 × 81
= 2 × 9
= 18
Hence, the x will be 18.
Question no – (10)
Solution :
In the given question,
24, 36, 36, x are in proportion
∴ x = 36 × 36/24
= 54
So, the x will be 54
Question no – (11)
Solution :
In the question we get,
The ratio of the number of boys to that of girls participating in a school is = 7 : 3.
The number of girls is = 165
Let the number of boys x
x : 165 = 7 : 3
x = 7 × 165/3
= 7 × 55
= 385
Hence, the number of boys will be 385.
Question no – (12)
Solution :
According to the question,
The ratio of the income to the expenditure of a family is = 7 : 6.
The income is = Rs 1400.
Saving = ?
Let, the expenditure of the family be = x
∴ 1400 : x = 7 : 6
∴ x = 1400 × 6/7
= 1200
∴ Saving = (Income – Expenditure)
= 1400 – 1200
= 200
Thus, his savings will be 200 Rs.
Question no – (13)
Solution :
In the question we get,
The ratio of sale of eggs on a Sunday to whole week = 2 : 9.
Total sale of eggs in the same week was = Rs 360
Let, the sale of egg in Sunday = x
⇒ 2 : 9 = x : 360
Now, x = 2 × 360/9
= 80
Thus, the sale eggs on Sunday will be 80
Question no – (14)
Solution :
According to the question,
The ratio of sale of pens to note book = 17 : 13,
The sale of pens is = Rs 850,
The sale of note book = ?
Let the sale of note book = x
∴ 17 : 13 = 850 : x
Now, x = 35 × 168/10
= 650
Hence, the sale of note book will be Rs 650.
Question no – (15)
Solution :
According to the question,
10 books costs Rs 35
The price of 16 books = ?
Let the price be = x
∴ 10 : 35 = 16 : x
Now,
x = 35 × 16 / 10
= 56
So, the price of 16 books will be Rs. 56
Question no – (16)
Solution :
From the question we know,
12 men can do piece of work in 45 days.
27 men do it in = ?
Let, x = number of days
∴ 12 : 27 = x : 45
Now,
x = 12 × 45/17
= 20 days
Therefore, 27 men will do it in 20 days.
Next Chapter Solution :
👉 Chapter 9 👈
