# S.chand mathematics solution class 8 chapter 10 Direct and inverse variation

## EXERCISE 10 A

Question 1

Given that y is directly proportional to x and y = 40 , when x = 200 . Find the value of
(i) y , when x = 15

Sol: (i)

y ∝ x ⇒ , where k is the constant of variation

Given , ⇒ k =

Also ,

[given: x=15]

= 3

(ii) x when y = 8

Sol: (ii)

y ∝ x ⇒ , where k is the constant of variation

Given , ⇒ k =

Also , 5y = x [given: y=8]

x = 40

Question 2

The length (in cm) stretched by a spring is directly proportional to the amount of force (in kg) applied . Given below are some observations about the force applied and the length stretched by a spring . Find the missing values in the table

 Force (in kg) Length stretched(in cm) 20 25 18 15 28

Sol:

As Force and Length vary directly . So is constant

∴The constant of variation

Now , = 24

Question 3

Priya takes 4 hours in walking a distance of 20 km . What distance would she cover in 7 hours ?

Sol:

Distance Time 20 km 4 hours 7 hours

As Distance ∝ Time ⇒

So is constant

∴The constant of variation = 5

Now ,

Distance = 7×5 = 35

ALTERNATE METHOD

As we know

= 5 km/hr

7 hours = 7×5 km

= 35 km

Question 4

If 15 burners consume 90 cubic metre of gas in 2 hours , how much will 9 burners consume in the same time ?

Sol:

Gas (m3) Burner 90 m3 15 9

As Gas consume ∝ Burner ⇒

So is constant

∴The constant of variation = 6

Now ,

Distance = 6×9 = 54

= 54 cubic metre or 54 m3

Question 5

The railway charges 5600 to carry a certain amount of luggage for 350 km . What should the charge be carry the same amount of luggage for 425 km ?

Sol :

Charges Distance (Km) 5600 350 km 425 km

As Charges ∝ Distance ⇒

So is constant

∴The constant of variation = 16

Now ,

Distance = 16×425 = 6800

Question 6

89 litres of oil cost 2091.50  . What is the cost of 15 litres ?

Sol :

 Oil Cost Litres 2091.5 89 15

As Cost ∝ Litres ⇒

So is constant

∴The constant of variation = 23.50

Now ,

Cost = 23.50×15 = 352.50

Question 7

68 packets weigh 1 kg 632 g . What will be weight of 70 packets ?

Sol :

Weigh Packets 1 kg 632 g (1632g) 68 70

As Weigh ∝ Packets ⇒

So is constant

∴The constant of variation = 24

Now ,

Cost = 24×70 = 1680 g

1680 g = 1 kg 680 g

Question 8

If a man working for 49 hours earns 1715 , how much will he earn working for 27 hours ?

Sol :

 Earns Hours (hours) 1715 49 27

As Earns ∝ Hours ⇒

So is constant

∴The constant of variation = 35

Now ,

Cost = 35×27 = 945

Question 9

The distance travelled by a ball dropped from an airplane is directly proportional to the square of time t . Given that t=2 seconds when d = 24 meters , find the distance the ball drops in 10 seconds .

Sol:

Distance (m) Time (sec) 24 m 2 sec 10 sec

As Distance ∝ Time ⇒

So is constant

∴The constant of variation = 12

Now ,

Distance = 12×10 = 120

= 120 metres

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