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**Maths Wiz Class 8 Solutions Chapter 9 Variations**

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Wiz Class 8 Math Book, Chapter 9, Variations. Here students can easily find step by step solutions of all the problems for Variations, Exercise 9A, 9B and 9C 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 9 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

**Variations Exercise 9A Solution : **

**Question no – (1) **

**Solution : **

**(a)** y/x = 3/1 = 6/2 = 9/3 = 12/4 = 3

**∴** y/x is a constant

**(b)** y/x = 16/10 = 8/5 = 7/3

**∴** y/x = is not a constant

**(c)** y/x = -8/4 = 2/-1 = 10/-5 = – 2

**∴** y/x is a constant

**Question no – (2) **

**Solution :**

**(a) y = – 7x**

= y/x = – 7 ….(constant)

**(b) 4x – 3y = 11**

= y/x is not identify a constant

**(c) – 8x + 5y = 0**

= -8x = – 5y

= y/x = 8/5 ….(constant)

**(d) xy = 9**

is not a identify a constant

**Question no – (3) **

**Solution : **

y varies directly with x

**∴**** **y = kx

x = 10, y = 12

12 = k × 10

= k = 12/10

= 6/5

When x = 25

**∴ **y = 6/5 × 25 = 30

**Question no – (4) **

**Solution : **

p varies directly as q

**∴** p = kq

p = 21, q = 7

21 = k.7

= k = 3

When p = 15

**∴** q = p/k = 15/3 = 5

Therefore, the q will be** 5**

**Question no – (5) **

**Solution : **

Direct variation equation

y/x = 68.75

y = 68.75x

**Question no – (6) **

**Solution : **

**(a)** Yes, the relationship is a direct variation

= -18x + 7y = 0

= -18x = 7y

= y/x = 7/18

= y = 7/18 x

**(b) **No, the relationship is not direct variation

= y – 20x = 2.50

**Question no – (7) **

**Solution : **

**(a) **y/x = 15

= y = 15x is a direct variation equation

**(b)** Given, x = 365 load laundry per year

**∴ **y = 15 × 365 = 5475l water she save at the end of a year.

**Question no – (8) **

**Solution : **

Yes, since the relation y = kx

**∴** Here k is constant then if x is double y is also gain double.

**Question no – (9) **

**Solution :**

In the given table air varies directly as time

**∴** y/x = 48/4 = 12

**∴** k = 12

**Now** if x = 3, y = 12 × 3

= 36 m

if y = 84, x = 84/12

= 7 min

if x = 25, y = 25 × 12

= 300 m

if y = 1860, x = 1860/12

= 155 min

**Question no – (10) **

**Solution : **

d varies directly as t

d = kt

d = 4, t = 9

4 = k9

= k = 4/9

t = 21, k = 4/9

d = 4/9 × 21 = 28/3

**Question no – (11) **

**Solution : **

bar |
mass |

40 cm | 420 g |

136 cm | ? (x) |

**∴** mass and bar varies directly

**∴** 40/136 = 420/x

= x = 420/40 × 136

= 1428 g

Therefore, the mass of a bar will be 1428 g.

**Question no – (12) **

**Solution : **

mass |
bend |

3 kg | 9 cm |

2 kg | x |

bend varies directly as the mass

3/2 = 9/x

= x = 9/3 × 2

= 6 cm

Hence, the pole will bend 6 cm for a 2 kg fish

**Question no – (13) **

**Solution : **

Bottles |
Children |

8 | 5 |

? x | 40 |

Children and bottles are at directly relation

8/x = 5/40

= x = 40 × 8/5

= 64

Thus, at the party there are 64 children.

**Question no – (14) **

**Solution : **

Steps |
Distance |

150 | 125 cm |

360 | x |

Step and distance varies directly

**∴ **150/360 = 125/x

= x = 125 × 360/150

= 300 cm

Hence, Harsh will cover 300 cm in 360 steps.

**Question no – (15) **

**Solution : **

Fare |
Journey |

125 | 240 km |

x | 144 km |

Fare and journey varies directly

**∴** 125/x = 240/144

= x = 125 × 144/240

= 75 rupees

**Variations Exercise 9B Solution : **

**Question no – (1) **

**Solution : **

**(a)** VP = k

= V = k/P

**(b)** I = k/R

= JR = k

**(c)** h = k/A

= hA = k

**(d)** f = k/l

= fl = k

**Question no – (2) **

**Solution : **

**(a) x and y vary directly**

**∴ **y/x = 11/3 = k

if y = 33 then x = y/k = 33 × 3/11 = 9

if x = 27 then y = 11/3 × 27 = 99

if y = 880 then x = 880 × 3/11 = 240

**(b) x and y vary directly**

**∴ **y/x = 6/30 = 1/5

if x = 15 then y = 15 × 1/5 = 3

if y = 2 then x = 2 × 5 = 10

if y = 1 then x = 1 × 5 = 5

**(c) x and y vary inversely**

xy = 2 × 48 = 96

if x = 3 then y = 32 × 1/3 = 32

if y = 16 then x = 96 × 1/16 = 6

if h = 8 then y = 96 × 1/8 = 12

**(d) x and y vary inversely**

xy = 1 × 125 = 125

if x = 5 then y = 125 × 1/5 = 25

if y = 5 then x = 125 × 1/5 = 25

if y = 1 then x =125 × 1 = 125

**Question no – (3) **

**Solution : **

**(a) y varies inversely as x**

**∴** xy = 2 × 9 = 18

when x = 3 then y = 18 × 1/3 = 6

**(b) u varies inversely as v**

uv = 12 × 3 = 36

when v = 9 then u = 36 × 1/9 = 4

**(c) c is inversely proportional to d**

cd = 18 × 2/3 = 12

when c = 6/7 then d = 12 × 7/6 = 14

**(d) m is inversely proportional to n**

mn = 0.02 × 5 = 0.1

if n = 0.2 then m = 0.1 × 1/0.2 = 1/2 = 0.5

**Question no – (4) **

**Solution : **

Speed |
Time |

12 km/hr | 20 min = 20/60 = 1/3 hr |

x | 15 min = 15/60 = 1/4 hr |

Speed and time varies inversely

**∴** 12 × 1/2 = 1/4 × x

= 4 = x/4

= x = 16 km/hr

**Question no – (5) **

**Solution : **

Speed |
Time |

72 km/hr | 10 hr |

x | 9 hr |

Speed and time varies inversely proportional

72 × 10 = 9 × x

= 72 × 10/9 = x

= x = 80 km/hr

**Question no – (6) **

**Solution : **

Pumps |
Time |

28 | 18 hr |

42 | x |

Pumps and time varies inversely

**∴** 28 × 18 = 42 × x

= x = 28 × 18/42

= x = 12 hr

Therefore, 42 such pumps do the same work in 12 hours.

**Question no – (7) **

**Solution :**

Person |
Days |

400 | 9 |

300 | x |

Person and days varies inversely

**∴** 400 × 9 = 300 × x

= x = 400 × 9/300

= 12 days

Therefore, the same stock will last 12 days for 300 persons.

**Question no – (8) **

**Solution : **

Persons |
Months |

630 | 14 |

x | 9 |

Persons and months are varies inversely

630 × 14 = x × 9

= x = 630 × 14/9

= x = 980 person

Therefore, had he to employ 980 extra person.

**Question no – (9) **

**Solution : **

Hours |
Days |

4 | 15 |

x | 10 |

Hours and days are varies inversely

**∴** 4 × 15 = x × 10

= x = 4 × 15/10

= x = 6 hours

**Question no – (10) **

**Solution : **

Speed |
Hour |

60 km/hr | 7.5 hr |

x | 6 hr |

Speed and hour are varies inversely

**∴** 60 × 7.5 = x × 6

= x = 60 × 7.5/6 × 10

= x = 75 km/hr

Hence, the required speed of the train will be 75 km/hr.

**Question no – (11) **

**Solution : **

Men |
Days |

800 | 39 |

(800) + 500 = 1300 | x |

Men and days are varies inversely

= 800 × 39 = x × 1300

= x = 800 × 39/1300

= 24 days

**Question no – (12) **

**Solution : **

Population |
Weeks |

22400 | 3 |

x | 7 |

Population and weeks are varies inversely

**∴** 22400 × 3 = 7 × x

= x = 22400 × 3/7

= 9600

**∴** (22400 – 9600) = 12,800 people must be sent away.

**Question no – (13) **

**Solution : **

Students |
Days |

500 | (60 – 12) = 48 |

(500 + 300) = 800 | x |

Students and days varies inversely

**∴** 500 × 48 = 800 × x

= x = 500 × 48/800

= 30 days

**Variations Exercise 9C Solution :**

**Question no – (1) **

**Solution : **

Men |
Hours |

6 | 12 |

9 | x |

men and hours varies inversely

6 × 12 = x × 9

= x = 6 × 12/9

= 8 hours

Hence, 9 men will take 8 hours to do the same work.

**Question no – (2) **

**Solution : **

Men |
days |

12 | 10 |

15 | x |

Men an days varies inversely,

12 × 10 = 15 × x

= x = 12 × 10/15

= 8 days

Therefore, 15 men will take 8 days to hoe the field.

**Question no – (3) **

**Solution : **

A can do a piece of work = 6 days

B can do a piece of work = 12 days

A’s 1 days work = 1/6

B’s 1 days work = 1/12

A and B combined work in 1 days

= 1/6 + 1/12

= 2 + 1/12

= 3/12

= 1/4

Hence, they both complete the work in 4 days.

**Question no – (4) **

**Solution : **

Rekha can finish a work in 18 days

Rekha’s 1 days work = 1/18

Prema can finish the work in 18/2 = 9 days

Prema’s one days work = 1/9

Rekha and Prema combined work in 1 day

= 1/18 + 1/9

= 2 + 2/18

= 3/18

= 1/6

Therefore, they can finish 1/6 of work in a day.

**Question no – (5) **

**Solution : **

A’s 1 day work = 1/12

B’s 1 day work = 1/24

A and B combined work in 1 day

= 1/12 + 1/24

= 2 + 1/24

= 3/24

= 1/8

A and B together complete the same work in 8 days

**Question no – (6) **

**Solution :**

A and B together can do 1 day work = 1/2

B’s 1 day work = 1/30

**A’s 1 day work, **

= 1/12 – 1/30

= 5-2/60

= 3/60

1/20

Therefore, A alone finish the work in 20 days.

**Question no – (8) **

**Solution :**

A and B together can do one day work = 1/72

B and C together can do one day work = 1/120

A and C together can do one day work = 1/90

**∴**** A, B and C can do one day work**

A + B + B + C + A + C = 1/72 + 1/120 + 1/90

= 2A + 2B + 2C = 30 + 18 + 24/2160

= A + B + C = 72/2160 × 2

= A + B + C = 1/60

and B + C = 1/120

**∴** A + 1/120 = 1/60

= A = 1/60 – 1/120

= A = 2 – 1/120

= A = 1/120

Therefore, A alone can do it in 120 days.

**Question no – (9) **

**Solution : **

A’s 1 day work = 1/10

B’s 1 day work = 1/20

C’s 2 days work = 2/10 = 1/5

A and B together one day work = 1/10 + 1/20 = 2+1/20 = 3/20

A and B can done the work in 0/3 days

A and B’s two days work = 2 × 3/20 = 3/10

A and B can do 10/3 days

**∴** 2 day work,

= 10/3 – 2 = 10-6/3 = 4/3

= 20/3 + 4/3

= 24

= 8 day will the whole work be completed.

Hence, the whole work will completed in 8 days.

**Question no – (10) **

**Solution : **

Piyush and Ajit together can complete the work in 3 days.

**∴** Piyush Ajit together can do 1 day work = 1/3

Piyush and Ajit together done the work 2 days and Piyush done the work = 2 days

Piyush and Ajit’s one day work = 1/2

**∴** work left = 1/2 – 1/3 = 3-2/6 = 1/6

Therefore, Piyush alone can complete it in 6 days.

**Question no – (12) **

**Solution : **

Suppose, Sanjoy left after x days

**∴ **x/45 + x+23/40 = 1

= 8x + 9x + 207/360 = 1

= 17x = 360 – 207

= x = 153/17

Therefore, After 9 days Sanjoy leave.

**Next Chapter Solution : **

👉 Chapter 10 👈