Rd Sharma Solutions Class 6 Chapter 9 Ratio Proportion and Unitary Method
Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Rd Sharma Class 6 Mathematics, Chapter 9, Ratio Proportion and Unitary Method. Here students can easily find Exercise wise solution for chapter 9, Ratio Proportion and Unitary Method. Students will find proper solutions for Exercise 9.1, 9.2, 9.3 and 9.4. Our teachers solved every problem with easily understandable methods so that every students can understand easily. Here all solutions are based on the CBSE latest curriculum.
Ratio Proportion and Unitary Method Exercise 9.1 Solution
Question no – (1)
Solution :
(i) So, the Ratio is,
= 2 : 3
(ii) Ratio of no of girls to boys
= 2 : 1
Question no – (2)
Solution :
(i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory.
(ii) The number of villages is 2000 times that of cities in India.
Question no – (3)
Solution :
(i) 60 : 72
= 5 : 6
(ii) 324 : 144
= 162 : 72
= 81 : 36
= 9 : 4
(iii) 85 : 391
= 5 : 23
(iv) 186 : 403
= 186/31 : 403/31
= 6 : 13
Question no – (4)
Solution :
(i) 75 paise to Rs 3
= 75 : 300
= 1 : 4
(ii) 35 minutes to 45 minutes
= 35 min : 45 min
= 7 : 9
(iii) 8 kg to 400 gm
= 8 kg : 400 gm
= 8000 : 400 gm
= 20 : 1
(iv) Given, 48 minutes to 1 hour
= 48 min : 1 h
= 48 : 60
= 8 : 10
= 4 : 5
Therefore, the ratio is 4 : 5
(v) Given, 2 metres to 35 cm
= 200 cm : 35
= 200 : 35
= 40 : 7
So, the ratio is 40 : 7
(vi) 35 minutes to 45 seconds
= (35 × 60) : 45
= 2100 : 45
= 420 : 9
= 140 : 3
Thus, the ratio is 140 : 3
(vii) Given, 2 dozen to 3 scores
= (2 × 12) : (3 × 20)
= 24 : 60
= 4 : 10
= 2 : 5
Hence, the ration is 2 : 5
(viii) 3 weeks to 3 days
= (3 × 7) : 3
= 21 : 3
= 7 : 1
So, the ration is 7 : 1
(ix) 48 min to 2 hours 40 min
= 48 : 160
= 6 : 20
= 2 : 5
So, the ratio is 2 : 5
(x) 3 m 5 cm to 35 cm
= 305 : 35
= 61 : 7
Thus, the ration is 61 : 7
Question no – (5)
Solution :
(i) 3.2 metres to 56 metres
= 32 : 56
= 32 : 560
= 4 : 70
= 2 : 35
So, the ratio is 2 : 35
(ii) 10 metres to 25 cm
= 1000 : 25 cm
= 40 : 1
So, the ratio is 40 : 1
(iii) 25 paise to Rs 60
= 25 : (60 × 100)
= 35 : 600
= 1 : 240
Thus, the ratio is 1 : 240
(iv) 10 litres to 0.25 litre
= 10 : 0:25
= 100 : 25
= 40 : 1
Therefore, the ratio is 40 : 1
Question no – (6)
Solution :
Boys : Girls
= 1168 : 1095
= 16 : 15
Now, HCF of 1168 and 1095 is 73
Therefore, the ration of boys and girls will be 16 : 15.
Question no – (8)
Solution :
(i) men to that of women,
No of men = 28, Total = 72
∴ Women = (72 – 28) = 44
∴ Men: Women,
= 28 : 44
= 7 : 11
(ii) men to the total number of persons
Men : Total persons
= 28 : 72
= 14 : 36
= 7 : 18
(iii) persons to that of women.
Persons : Women
= 72 : 44
= 18 : 11
Question no – (9)
Solution :
Tape, Length = 10m
= (10 × 100)
= 1000 cm
Width = 2.4 cm
= 2.4 cm
∴ Length : Width
= 100 : 2.4
= 10000 : 24
= 1250 : 3
Therefore, ratio of its length to width is 1250 : 3
Question no – (10)
Solution :
According to question,
Office time 9 am to 5 pm = 8 hours duration
30 min lunch interval
∴ Working time
= (8 × 60 – 30) min
= (480 – 30) mon
= 450 min
∴ Lunch time : Total duration
= 30 : 480 min
= 1 : 16
Therefore, the ratio of lunch interval will be 1 : 16.
Question no – (11)
Solution :
Bullock cart travels,
= 3 h – 24 km
= 1 h – 24/3 km
= 8 km/hr
Train travels,
= 2 h – 120km
= 1 hr – 120/2
= 60 km/hr
∴ Ratio
= 8 : 60
= 2 : 15
Hence, the ratio of their speeds will be 2 : 15.
Question no – (12)
Solution :
(i) her savings to her income
Margarette, savings : Income
= 185 : 955
= 37 : 191
(ii) her income to her expenditure
= Expenditure
= (955 – 185) Rs
= 770 Rs
∴ Income : Expenditure
= 955 : 770
= 191 : 154
(iii) her savings to her expenditure
Savings : Expenditure
= 185 : 770
= 37 : 154
Ratio Proportion and Unitary Method Exercise 9.2 Solution
Question no – (1)
Solution :
(i) Given, 3/4 or 9/16
L.C.M of 40 16 is = 16
∴ 3/4 × 16 = 12
= 9/16 × 16 = 9
∴ 12 > 9
Here 3/4 is the larger one
(ii) Given, 15 : 16 or 24 : 25
= 15/16 or 24/25
= L.C.M of 16 and 25 is 400
∴ 15/16 × 400 = 375
= 24/25 × 400 = 384
∴ 384 > 375
Thus, 24 : 25 is the larger one.
(iii) Given, 4 : 7 or 5 : 8
= 4/7 or 5/8
∴ L.C.M of 7,8 is 56
= 4/7 × 56 = 32
= 5/8 × 56 = 35
∴ 35 > 32
∴ 5/8 > 4/7
Question no – (2)
Solution :
Given 6 : 8 = 6/8
= 6/8 × 2/2 = 12/16
= 6/8 ÷ 2/2 = 3/4
So, Equivalent ratio are 12/16 and 3/4
Question no – (3)
Solution :
= 12/20 = 3/5 = 9/15
Ratio Proportion and Unitary Method Exercise 9.3 Solution
Question no – (1)
Solution :
(i) 16 : 24 = 20 : 30
= 16 : 24 = 20 : 30
= 4/6 = 4/6
= 2/3 = 2/3
∴ This is true
(ii) 21 : 6 = 35 : 10
= 21/6 = 35/10
= 7/2 = 7/2
∴ This is true
(iii) 12 : 18 = 28 : 12
= 12/18 = 28/12
= 2/3 ≠ 7/3
∴ 2/3 ≠ 7/3
So, this is not true
(iv) 51 : 58 = 85 : 102
= 51/58 = 85/102
= 51/58 ≠ 5/6
∴ This is not true
(v) 40 men : 200 men = Rs 5 : Rs 25
= 40/200 = 5/25
= 1/5 = 1/5
∴ This statement is true.
Question no – (2)
Solution :
(i) 8, 16, 6, 12
So, 8 : 16 = 8/16 = 1/2
and, 6/12 = 1/2
∴ This are in proportion
(ii) 6, 2, 4, 3
Now, 6 : 2 = 3 : 1
= 4 : 3
∴ 3 : 1 ≠ 4 : 3
So, there are not in Proportion
(iii) 150, 250, 200, 300
= 150 : 250 = 15 : 25 = 3 : 5
= 200 : 300 = 2 : 3
∴ 3 : 5 ≠ 2 : 3
∴ They are not proportion.
Question no – (3)
Solution :
(i) x : 6 = 55 : 11
= x/6 = 55/11
= 11x = 6 × 55
= x = 6 × 55/11
∴ x = 30
(ii) 18 : x = 27 : 3
= 18/x = 27/3
= 27x = 3 × 18
= x = 3 × 18/27
∴ x = 2
(iii) 7 : 14 = 15 : x
= 7/14 = 15/x
= 7x = 14 × 15
= x = 14 × 15/7
∴ x = 30
(iv) 16 : 18 = x : 96
= 16/18 = x/96
= x = 69×16/18
= 128/3
∴ x = 128/3
Question no – (5)
Solution :
(i) Given, 45 : 30 = 24 : 16
Now, 45 : 30 = 3 : 2/24 : 16 = 3 : 2
45 : 24 = 30 : 16 can be written 15 : 8
30 : 45 = 16 : 24 can be written 2 : 3
16 : 30 = 24 : 45 can be written as 8 : 15
Question no – (6)
Solution :
Here, 4, x, 9 are in continued proportion
Now, 4 : x : : x : 9
= 4/x = x/9
= x2 = 4 × 9
= x = √36
∴ x = 6
Therefore, the value of x will be 6.
Question no – (7)
Solution :
Let, x is the third term,
∴ 32 : 112 : : x : 217
= 32/112 = x/217
= x = 217 × 32/112
= x = 62
Therefore, the third term will be 62.
Question no – (8)
Solution :
(i) 36, 90, 225
∴ 36/90 = 6/15 = 2/5
and, 90/225 = 2/5
∴ 36 : 90 : : 90 : 225
(ii) 48, 60, 75
∴ 48/60 = 4/5
and, 60/75 = 4/
∴ 48 : 60 : : 60 : 75
(iii) 16, 84, 441
∴ 16/84 = 4/21
= 84/441 = 4/21
∴ 16 : 84 : 84 : : 84 : 441
Question no – (9)
Solution :
Length : Width = 5 : 2
Given width = 40m
∴ 2 – 40
= 5 – 40/2 × 5
= 100
Therefore, the Length of the school garden will be 100 m.
Question no – (10)
Solution :
Sunday sale : sale of whole weak
= 2 : 9
Total egg sale 360 in weak
So, 9 – 360
= 1 – 360/9
∴ 2 – 360/9 × 2
= 80 eggs
Therefore, the sale of egg Sunday 80 eggs.
Question no – (11)
Solution :
Copper : Line = 9 : 7
∴ 7 unit = 9 : 8
= 1 unit = 9.8/7
∴ 9 unit = 9.8 × 9/7
= 12.6
Hence, the weight of copper will be 12.6 kg.
Question no – (12)
Solution :
Income : Expenditure = 7 : 6
Let, income 7x and Expenditure 6x
Income is 1400
So, 7x = 1400
= x = 1400/7
= 200
∴ Savings,
= (7x – 6x)
= x
= 200 Rs
Therefore, the savings will be 200 Rs.
Question no – (13)
Solution :
According to question,
Story books : other books = 1 : 7
Let, story books x and other books 7x
Total story books = 800
∴ other books
= 7x = (7 × 800)
= 5600
∴ Total books,
=(800 + 5600)
= 6400 books
Therefore, the total number of books in the library is 6400.
Ratio Proportion and Unitary Method Exercise 9.4 Solution
Question no – (1)
Solution :
According to the question,
Price of 3 m cloth = 79.50 Rs
Price of 1 m cloth = 79.50/3 Rs
∴ Price of 15 m cloth,
= 79.50 × 50/3
= 397.50 Rs
Thus, the price of 15 metres of such cloth is 397.50 Rs.
Question no – (2)
Solution :
According to question,
In 9605 Rs, no of chairs purchased = 17
In 1 Rs no of chairs purchased = 17/9605
∴ In 56500 no of chairs purchased,
= 17 × 56500/9605
= 100 chairs.
Hence, 100 chairs can be purchased in Rs 56500.
Question no – (3)
Solution :
As per the question,
3 Ferryloads carry 150 people
∴ 1 ferryloads carry 150/3 people
∴ 4 ferryloads carry,
= 150 × 4/3
= 200 people
Therefore, 200 people will be carried on 4 ferryloads.
Question no – (4)
Solution :
As per the question,
Cost of 9 kg rice = 120.60 Rs
Cost of 1 kg rice = 120.60/9 × 50
∴ Cost of 50 rice,
= 120.60/9 × 50
= 670 Rs
Therefore, 50 kg of such a quality of rice will cost 670 Rs.
Question no – (5)
Solution :
According to the question,
Distance travelled by train in 5 h = 200 km
Distance travelled by train in 1h = 200/5km
∴ Distance travelled buy train in 7h,
= (40 × 7) km
= 280 km
Therefore, it will run 280 km in 7 hours.
Question no – (6)
Solution :
As per question,
10 boys dig a pitch in = 12 h
∴ 1 boy dig a pitch in,
= (10 × 12) h
∴ 8 boys dig a pitch in,
= 120/8 h
= 15 h
Thus, 8 boys take 15 h to do it.
Question no – (7)
Solution :
As per the question,
A men work 8 h daily finish works in = 12 days
A men work 1 h daily finish work in,
= (8 × 12) day
∴ A men work 6 h daily finish work in,
= 8 × 12/6
= 16 days
Therefore, the same work will be finished in 16 days.
Question no – (8)
Solution :
According to the question,
Cost of 15 post cards = 2.25 Rs
Cost of 1 post cards = 2.25/15 Rs
∴ Cost of 36 post card’s
= 2.25 × 36/15
= 5.40 Rs
∴ In 1 Rs post card can buy,
= 15/2.25
∴ In 45 Rs post card’s can buy,
= 15/2.2 × 45
= 300 post cards
Hence, 300 postcards we can buy in Rs 45.
Question no – (9)
Solution :
Cost of rail journey of 75 km = 215 Rs
Cost of rail journey of 75 km = 215/75
∴ cost of rail journey of 120 km,
= 215 × 120/75
= 344 Rs
So, journey of 120 km will cost 344 Rs
Question no – (10)
Solution :
As per the question,
Sales tax on a purchase worth Rs 60 = 4.20 Rs
Sales tax on a purchase worth Rs 1 = 4.20/60
∴ Sales tax a purchase worth Rs 150,
= (4.20/60 × 150)
= Rs 10.50
Therefore, sales tax on the purchase worth Rs 150 will be 10.50 Rs.
Question no – (11)
Solution :
1st, number of chairs purchased in Rs 19210 = 17
∴ Number of chairs purchased in Rs 1 = 17/19210
∴ Number of chairs purchased in Rs 113000
= 17/19210 × 11300
= 100 chairs
Thus, 100 such chairs can be purchased.
Question no – (12)
Solution :
1st we need to find Speed of the car,
= 165/3
= 55 km/hr
∴ Time take to travel 440 km
= 440/55
= 8h
∴ Distance curved in 7h,
= (55 × 7)
= 385 km
Therefore, the car will take 8 hours to travel 440 km, and it will travel 385 km in 7 hours.
Question no – (13)
Solution :
Cost of 2 dozen,
= 24 oranges (1 dozen = 12)
= 60 Rs
∴ Cost of 1 dozen oranges = 60/24
∴ Cost of 120 oranges,
= 60/24 × 120
= 300 Rs
Therefore, the cost of 120 similar oranges is 300 Rs.
Question no – (14)
Solution :
As per the question,
Sugar used by 4 members family = 6kg
∴ Sugar used by 1 members family
= 6/4 kg
∴ Sugar used by 6 members family,
= (6/4 × 6) kg
= 9 kg
Hence, the monthly consumption of sugar will be 9 kg.
Question no – (15)
Solution :
According to the given question,
No of folding chairs weighing 18 kg = 45
No of folding chairs weighing 1 kg = 45/18
∴ No of folding chairs weighing = 4000
= 45/15 × 4000
= 10,000
Therefore, 10,000 such chairs can be loaded on truck.
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