myhelper: S.chand publication New Learning Composite mathematics solution of class 8 Chapter 9 Variation Exercise 9A

Exercise 9A

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Question 1

Tell whether each relationship is a direct variation. Explain. If yes, state the constant of variation.

(a)

x	1	2	3	4
y	3	6	9	12

Sol :

$\frac{x}{y}=\frac{1}{k}=\frac{1}{3}=\frac{2}{6}=\frac{3}{9}=\frac{4}{12}=\frac{1}{3}$

∴$\frac{y}{x}=k=3$

∴It is direct variation

(b)

x	10	5	3
y	16	8	7

Sol :

$\frac{x}{y}=\frac{1}{k}=\frac{10}{16}=\frac{5}{8}\neq \frac{3}{7}$

∴$\frac{y}{x}=k$

∴It is not direct variation

(c)

x	4	-1	-5
y	-8	2	10

Sol :

$\frac{x}{y}=\frac{1}{k}=\frac{4}{-8}=\frac{-1}{2}=-\frac{5}{10}=-\frac{1}{2}$
∴$k=-\frac{1}{2}$

∴It is direct variation

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Question 2

Tell whether each relationship is a direct variation. Explain. If yes, state the constant of variation.

(a) y = -7x

Sol :

$\frac{y}{x}=-7=k$

[constant] yes

(b) 4x – 3y = 11

Sol :

4x=1+3y

No constant

Sol :

$\frac{y}{x}=\frac{8}{5}=k$

[constant]

(d) xy = 9

Sol :

$y=\frac{a}{x}$

[no constant]

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Question 3

The value of y varies directly with x, and y = 12 when x = 10, Find y when x = 25.

Sol :

y ∝ x

∴y=kx

Now, y=12, x=10 ∴$k=\frac{12}{10}=\frac{6}{5}$

∴x=25, $y=\frac{6}{5}\times 25=30$

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Question 4

If p varies directly as q and if p = 21 when q = 7, then find q when p = 15.

Sol :

p ∝ q

$\frac{p}{q}=k$

when, p=21, q=7

$k=\frac{21}{7}=3$

∴Now , p=15

∴$\frac{p}{q}=k$

$q=\frac{p}{k}=\frac{15}{3}=5$

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Question 5

If the cost of petrol is Rs. 68.75 per litre, write a direct variation equation to describe the cost y of x litres of petrol.

Sol :

Y=68.75x

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Question 6

Tell whether each relationship is a direct variation. Explain your answer.

(a) The equation -18x + 7y = 0 relates the length of a videotape in centimeters x to its approximate playing time in seconds y.

Sol :

-181x+7y=0

-18x=-7y

$\frac{x}{y}=\frac{7}{18}$

∴$\frac{y}{x}=\frac{18}{7}=k$

∴y ∝ x

∴y=kx

It is a direct variation

(b) The equation y – 2.00x = 2.50 relates the cost y of a taxicab journey to distance x in km covered by the cab.

Sol :

y=-2.00x=2.50

∴No, it is not direct variation because it cant be written like

y=kx

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Question 7

Ragini bought an energy efficient washing machine. She will save about 15 litres of water per wash load.

(a) Write an equation of direct variation to describe how many litres of water y Ragini saves for x loads of laundry she washes.

(b) If Ragini does one load of laundry daily, how many litres of water will she save at the end of a year?

Sol :

(a) y=15x

(b) y=15x=15×365=5475L

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Question 8

Think and answer. If you double an x-value in a direct variation, will the corresponding y-value double? Explain.

Sol :

According to direct variation

If x value is double, then corresponding y value will be double also.

∵y=kx

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Question 9

The height of which a balloon and hydrogen gas rises in the air varies directly as time. Given below are some observations about the time and the corresponding height of the balloon (in metres). Find the missing terms in the table.

Time (in minutes)	3	4	_	25	_
Height of the Balloon (in metres)	_	48	84	_	1860

Sol :

Let, Time=x

Height=y

y ∝ x
∴y=kx

∵$k=\frac{48}{4}=12$

Time (in minutes)	3	4	7	25	155
Height of the Balloon (in metres)	36	48	84	300	1860

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Question 10

If d varies directly as t, and if d = 4 when t = 9, find d when t = 21.

Sol :

d ∝ t

∴d=kt

d₁=4 , t₁=9

d=kt

∴ $k=\frac{d_1}{t_1}=\frac{4}{9}$

Again , t₂=21

∴ d₂=k.t₂ $=\frac{4}{9}\times 21=\frac{28}{3}$

$d_2=\frac{28}{3}$

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Question 11

The mass of a uniform copper bar varies directly as its length. If a bar 40 cm long has a mass of approximately 420 g. Find the mass of a bar 136 cm long.

Sol :

m₁=420g ,L₁=40cm

m ∝ L

$k=\frac{m}{L}$

∴m₁=kL₁

$k=\frac{m1}{L1}=\frac{420}{40}=\frac{21}{2}$

Now, L₂=136cm

$k=\frac{21}{2}$

∴m₂=kL₂$=\frac{21}{2}\times 136=1428g$

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Question 12

A fish with a mass of 3 kg causes a fishing pole to bend 9 cm. If the amount of bending varies directly as the mass, how much will the pole bend for a 2 kg fish?

Sol :

Let, Bending=b

mass=m

According to question

b ∝ m

∴b=k m

Now , b₁=9 cm , m₁=3kg

∴$k=\frac{b1}{m1}=\frac{9}{3}=3$

again, m₁=2kg

b₂=k m2

or b₂=2×3=6cm

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Question 13

At a party, 8 bottles of soft drink are served for every batch of 5 children. How many bottles would be served if 40 children were present at the party?

Sol :

Bottles =B₁=8 bottles

Children=C₁=5 Children

B ∝ C

Now ,B₁=k C₁

or $k=\frac{8}{5}$

again , C₂=40

∴B₂=k C₁

or $B_2=\frac{8}{5}\times 40=64$ bottles

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Question 14

Harsh takes 150 steps in walking distance of 125 metres. What distance would he cover in 360 steps?

Sol :

D ∝ S

D=kS

Now , S₁=150 steps , D₁=125 m

$k=\frac{125}{150}=\frac{5}{6}$

Again , S₂=360 steps

D₂=k S₂$=\frac{5}{6}\times 360$

=300 m

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Question 15

The second class railway fare for 240 km of journey is Rs. 125. What would be the fare for a journey of 144 km? Assume that the fare varies directly as the length of the journey.

Sol :

D ∝ M

∴D=kM

Now , D₁=240m M₁=125

∴$k=\frac{D_1}{M_1}=\frac{240}{125}=\frac{48}{25}$

again, D₂=144 km

∴$m_2=\frac{D_2}{k}=144\times \frac{25}{48}$

=75

S.chand publication New Learning Composite mathematics solution of class 8 Chapter 9 Variation Exercise 9A

Exercise 9A

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

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