**Class 8 ICSE Maths Solutions Chapter 10 Direct and Inverse Variations (Selina Concise)**

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Selina Class 8 ICSE Math Book, Chapter 10, Direct and Inverse Variations. Here students can easily find step by step solutions of all the problems for Direct and Inverse Variations, Exercise 10A, 10B, 10C, 10D and 10E 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. Here in this post students will get chapter 10 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

**Direct and Inverse Variations Exercise 10(A) Solution :**

**Question no – (1) **

**Solution : **

**(i) From questions,**

x_{1}/y_{1} = 3/4.5 = 1/1.5

x_{2}/y_{2} = 5/7.5 = 1/1.5

x_{3}/y3 = 8/12 = 1/1.5

x_{4}/y_{4} = 11/16.5 = 1/1.5

x_{1}/y_{1} = x_{2}/y_{2} = x_{3}/y_{3} = x4/y4

x and y vary directly

**(ii) From questions,**

x_{1}/y_{1} = 16/30 = ½

x_{2}/y_{2} = 30/60 = ½

x_{3}/y_{3} = 40/80 = ½

x_{4}/y_{4} = 56/84 = ½

x and y are not in direct variation

**(iii) From question,**

x₁/y₁ = 27/81 = 1/3

x₂/y₂ = 45/180 = 1/3

x_{3}/y_{3} = 54/216 = ¼

x_{4}/x_{5} = 75/225 = 5/15

= 1/3

**Question no – (2) **

**Solution : **

Here, x and y are in direct variation,

3/36 = x/60 = y/96 = 10/z

= 3/36 = x/60, 3/36 = y/96, 3/36 = 10/z

= x = 60 × 3/36,

= 5

y = 96 × 3/36

= 8

z = 36 × 10/3

= 120

**Question no – (3) **

**Solution : **

Let, the distance will cover x km,

**∴** 28/448 = 64/x

= x = 448 × 64/28

= 1024 km

Therefore, it will cover 1024 km in 64 litres of diesel.

**Question no – (4) **

**Solution : **

Let, charge x

Here, it is in direct variation,

**∴ **18000/100 = x/120

= x = 120 × 1800/100

= 2160

Hence, it will charge Rs.2160 for a journey of 120 km.

**Question no – (5) **

**Solution :**

Let, bought articles x

It is direct variation.

Since, 1890/27 = 1750/x

= x = 1750 × 27/1890

= 25 articles.

Therefore, 25 articles can be bought for Rs. 1,750.

**Question no – (6) **

**Solution :**

Here, Let, x kg rice bought

**∴** 7 : 1120 :: x : 3680

**∴** x = 7 × 3680/1120

= 23 kg rice.

Therefore, 23 kg can be bought for Rs. 3,680.

**Question no – (7) **

**Solution :**

Let, the cost of note-books x

So, 6 : 156 : : 54 : x

= 6/156 = 54/x

= x = 156 × 54/6

= 1404 Rs.

Therefore, the cost of 54 such note-books 1404 Rs.

**Question no – (8) **

**Solution :**

Let, x men should be employed,

**∴** 22 : 27 : : x : 135

= 22/27 = x/135

= x = 135 × 22/27

= 110 men.

Thus, 110 men should be employed.

**Question no – (9) **

**Solution : **

Let, articles x.

**∴** 11 : 77 : : x : 224

= x = 11 × 224/77

= 32 articles.

Therefore, 32 articles would weight 224 kg.

**Question no – (10) **

**Solution : **

**(i)** Train 60 minutes cover 120 km.

1 minute cover 120/60

36 minutes cover = 120 × 36/60

= 72 km.

Hence, it will go 72 km in 36 minutes

**(ii)** 120 km cover 60 minutes.

1 km cover 60/120 minutes

210 km cover = 60 × 210/120

= 105 minutes

I.C = 1 hour 45 minutes.

Therefore, it will take 1 hour 45 minutes to cover 210 km.

**Direct and Inverse Variations Exercise 10(B) Solution :**

**Question no – (1) **

**Solution :**

Here, x and y are inversely proportional the xy are equal.

**(i) xy = 4 × 6 = 24**

x y = 3 × 8 = 24

xy = 12 × 2 = 24

xy = 1 × 24 = 24

**∴** xy are equal.

Therefore, x and y are inversely proportional.

**(ii) xy = 30 × 60 = 1800**

xy = 120 × 30 = 3600

xy = 60 × 30 = 1800

xy = 24 × 75 = 1800

Therefore, xy are not equal so it is not inversely proportional

**(iii) xy = 10 × 90 = 900**

xy = 30 × 30 = 900

xy = 60 × 20 = 1200

xy = 10 × 90 = 900

**∴** xy is not equal

Therefore, x and y not inversely proportional.

**Question no – (2) **

**Solution : **

Here, ∵ x and y are inversely proportional.

**∴** xy is equal.

**(i) xy = 4 × 4 = 16**

xy = 8 × l = 16

= l = 16/8

= 2

= 2 × m = 16.

= m = 16/2 = 8

32 × 12 = 384

= n = 16/32 = 1/2

**(ii) xy = 32 × 12 = 384**

24 × l = 384

= l = 384/24

= m × 8 = 384

= m = 384/8

= m = 48

16 × n = 384

= n = 384/16

= n = 24

**Question no – (3) **

**Solution :**

Here, M_{1} : D_{1} : : M_{2} : D_{2}

= 36 : 7 : : X : 42

It is inversely proportional,

36 × 7 = x × 42

= x = 36 × 7/42

= 6 men

Therefore, 6 men will do the same work in 42 days.

**Question no – (4) **

**Solution :**

Here, pipes : time : pipes : time

= 12 : 2x : : 21 : 42

By inverse proportion,

12 × 42 = 21 × x

= x = 12 × 42/21

= 24 minutes.

Hence, it will take24 minute to fill the same tank.

**Question no – (5)**

**Solution : **

Given, 150 men had provisions for 45 days.

After 10 days,

150 men, provision will last,

= (45 – 10)

= 35 days.

1 men provision will last,

= (150 × 35) days

And (150 – 25) = 125 men provision will last

= 150 × 35/125

= 42 days.

Therefore, the food will last 42 days at the same rate.

**Question no – (6) **

**Solution :**

Here, M_{1} : D_{1} : : M_{2} : D_{2}

= 72 : 25 : : 30 : x

By inverse proportion,

72 × 25 = 30 × x

= x = 72 × 25/30

= 60 days.

Therefore, 30 men will complete the same work in 60 days.

**Question no – (7) **

**Solution **

Here, Let workers required x.

W_{1} : H_{1} : : W_{2} : H_{2}

= 56 : 180 : : x :70

By inverse proportion,

56 × 180 = x × 70

= x = 56 × 180/70

= 144 workers.

Thus, 144 workers will be required to complete the same work in 70 hours.

**Question no – (8) **

**Solution :**

Let, time taken x hour.

T_{1} : D_{1} : : T_{2} : D_{2}

= 6 : 50 : : x : 75

By inverse proportion,

6 × 50 = x × 75

= x = 50 × 6/75

= 4 hour.

Therefore, It will take 4 hour when the car travels at the speed of 75 km per hour.

**Direct and Inverse Variations Exercise 10(C) Solution :**

**Question no – (1) **

**Solution : **

As per the given question,

Cost 24 identical articles = 108 Rs

Cost of 1 article = 108/24

**∴** Cost of 40 articles,

= (108/24 × 40)

= 180 Rs

Therefore, the cost of 40 similar articles will be 180 Rs.

**Question no – (2) **

**Solution :**

According to the given question,

15 men can work in 30 days.

1 men can work in 30 × 15

**∴** 18 men can work in,

= 30 × 15/18

= 25 days.

Hence, 18 men will complete it in 25 days.

**Question no – (3) **

**Solution : **

To complete a work in,

28 days men required 60

1 day men required 60 × 28.

**∴** 40 days men required’,

= 60 × 28/40

= 42

Therefore, 42 men required to complete the work in 40 days.

**Question no – (4)**

**Solution : **

450 soldiers provision for (40 – 10) = 30 days.

1 soldier provision for = (30 × 450)

**∴** 540 soldiers provision for,

= 30 × 450/540

= 25 days.

Therefore, the remaining provisions will last 25 days at the same rate.

**Question no – (5)**

**Solution : **

Here, strength of garrison = 480 men

Reduced by = 160 men

New strength of garrison,

= (480 – 160)

= 320

480 men provision for 12 days.

1 men provision for 12 × 480

**∴** 320 men provision for,

= 12 × 480/320

= 180 days.

Therefore, provisions will last for 180 days.

**Question no – (6) **

**Solution ****: **

**(i)** 3/5 quintal of wheat cost = 210

**∴** 1 quintal of wheat cost,

= 210 × 5/3

= 350 Rs.

**∴** The cost of 1 quintal of wheat will be 350 Rs.

**(ii)** 0.4 quintal of wheat cost,

= 350 × 0.4

= 140

∴ The cost of 0.4 quintal of wheat will be 140 Rs.

**Question no – (7) **

**Solution : **

As per the question,

2/9 of a property cost = 252000

1 of a property cost = 252000 × 9/2

**∴** 4/7 of a property cost,

= 252000 × 9/2 × 4/7

= 648000 Rs

Hence, the cost of 4/7 of it will be 648000 Rs.

**Question no – (8) **

**Solution : **

**(i)** Here, 4 men can earn 360 in one day.

**∴** 1 men can earn 360/4 in one day.

= 90 Rs in one day.

**(ii)** 6 women earn 360 in one day.

1 woman 360 in one day 360/6

= 60 Rs

**(iii)** 6 man 8 4 women earn in one day.

= (6 × 90 + 4 × 60)

= (540 + 240)

= 780 Rs

**Question no – (9) **

**Solution : **

16 boys pay bill = 114.40 Rs

1 boy pay bill = 114.40/16 Rs

= 7.15 Rs

**∴** Contribution of a boy who pays for himself and 5 others,

= (6 × 7.15)

= Rs 42.90

**Question no – (10) **

**Solution : **

According to the given question,

In 16 days digging pond labour required = 50

In 1 days digging pond labours required= 50 × 16

In 20 days dinging pond labour required = 50 × 16/20

**∴** In 20 days dinging pond double work required,

= 50 × 16 × 2/20

= 80

Therefore, the required labour will be 80

**Question no – (13) **

**Solution : **

Given, 6 m and 6 w can finish work in 24 days.

144 m and 144 w can finish work 1 day.

8 m and 12 work can finish work 15 days

120 m and 180 w can finish work in 24 days.

**(i)** 144 men + 144 women = 120 men + 180 women

= 144 men – 120 men = 180 women – 144 women

= 24 men = 36 women

= 1 man = 36/24

1 man = 3/2 woman

**(ii)** In first, 36 × 3/2 + 6

= 9 + 6

= 15 women

In second case, 4 × 3/2 + 6 = 12 woman

15 w can do piece of work in 24 days

1 w can do piece of work in 24 × 15

**∴** 12 w can do piece of work in,

= 24 × 15/12

= 30 days

**Direct and Inverse Variations Exercise 10(D) Solution :**

**Question no – (1) **

**Solution : **

In 10.40 orange bought 8 pc

1 orange bought 8/10.40

**∴** 16.90 orange bought,

= 8/10.40 × 16.90

= 13

**∴** Number of more orange which can bought

= (13 – 8)

= 5

Therefore, he can bought 5 more oranges.

**Question no – (2) **

**Solution : **

As per the given question,

In 60 days wall can build by 15 men

1 day wall can build by 15 × 60

**∴** 45 days wall can build by,

= 15 × 60/45

= 20 men.

**∴** Number of more man required to build the wall in 45 days,

= (20 – 15)

= 5 man

Thus, 5 more men are required to build another wall.

**Question no – (3) **

**Solution : **

Working condition taps = (6 – 2) = 4

6 taps can fill empty cistern 8 hours

1 tap can fill empty cistern = 6 × 8 hours

4 taps can fill empty cistern,

= 6 × 8/4

= 12

**∴** More time take when 2 taps out of order,

= (12 – 8)

= 4 hours.

Hence, more 4 hours time will be taken.

**Question no – (5) **

**Solution : **

Given in the question,

10 hours consume 18 bushels in 36 days.

1 hour consume 18 bushels in 36 × 10

**∴** 30 hours consume 18 bushels in,

= 36 × 10/30

= 12 days

30 hours consume 1 bushels in 12/18 days

**∴** 30 hours consume 24 bushels in,

= 12/18 × 24

= 16 days

Therefore, 24 bushels last 16 days for 30 horses.

**Question no – (6) **

**Solution : **

Family of persons can be maintain with Rs 6944,

= (20/240 × 6944)

= 56 days

Family of 1 person can be maintained,

= (56 × 5)

= 280 days

Family of 8 person can be maintained,

= 56 × 5/8

= 7 × 5

= 35 days

Hence, it will maintain the family for 35 days.

**Question no – (7) **

**Solution : **

In 1 day working 8 hours a day work complete by = 90 × 24/18 × 8

**∴** 1 hour working 8 hours a day work complete by = 90 × 24/18 × 8

**∴** 7/1/2 hours working 8 hours a day work complete,

= 90 × 24 × 8/18 × 2/15

= 128 men

Thus, 128 men are required to complete the same work.

**Question no – (8) **

**Solution : **

According to the given question,

12 typists can type in 18 days with 8 working hours.

1 typists can type in 18 days with = (8 × 12)

**∴** 1 typists can type in 9 days with,

= 2 × (8 × 12)

= 2 × 96

**∴** 16 typists can type in a day,

= 2 × 96/16

= 12 hours.

Therefore, the sixteen typists must work 12 hours per day in order to complete the work.

**Question no – (9) **

**Solution :**

As per given question,

25 horses consume 18 quintal in 36 days.

1 horses consume 1 quintal in 36 × 25/18

**∴** 30 horses consume 28 quintal in,

= 36 × 25 × 28/18 × 30

= 140/3

= 46 2/3 days.

Therefore, 28 quintal will last 46 2/3 days for 30 horses.

**Question no – (10) **

**Solution : **

According to question,

70 men dig 15000 sq m field in 5 days,

**∴** 1 men dig 15000 sq. m field in 5 × 70/15000 days

**∴** men required to dig 22,500 sq. m in 25 days,

= 5 × 70 × 22500/15000 × 25

= 70 × 900/3000

= 21

Hence, 21 man will required to dig 22500 sq. m field in 25 days.

**Question no – (12) **

**Solution : **

Work finish = 5/21 part

Remaining = (4 – 5/21)

= 21 – 5/21

= 61/21

5/21 work can done in 6 days working 10 hours a day by 10 m

1 work can done in 6 days working 10 hours a day 10 × 21/5

1 work can done in 1 day working 10 hours a day = 10 × 21 × 6/5

**∴** 16/21 work can done in 8 days working 10 hours a day,

= 10 × 21 × 6 × 16/5 × 21 × 8

= 24 men.

Therefore, 24 men will be required to complete the remaining work in 8 days.

**Question no – (13) **

**Solution :**

Work finish = 5/21 part

Remaining = (4 – 5/21)

= 21 – 5/21

= 61/21

5/21 work can done in 6 days working 10 hours a day by 10 m

1 work can done in 6 days working 10 hours a day 10 × 21/5

1 work can done in 1 day working 10 hours a day = 10 × 21 × 6/5

**∴** 16/21 work can done in 8 days working 10 hours a day,

= 10 × 21 × 6 × 16/5 × 21 × 8

= 24 men.

Therefore, 24 men will be required to complete the remaining work in 8 days.

**Next Chapter Solution : **

👉 Chapter 11 👈