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7/29/2019 Exercise.mt

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4.1

1.a) If x y and x=20 when y = 5 find (i) constant of variation (ii) the equation of variation.b) If y x and x= 7 and y 21 find (i) constant of variation (ii) the equation of variation (iii) the

value of y when x = 9.

c) m varies directly as n and m=27 when n = 18, find (i) the value of n when m = 15 (ii) thevalue of m when n =57.

d) If y x and x=12 when y = 18. Find (i) constant of variation (ii) the equation of variation (iii)the value of x when y = 75 (iv) the value of y when x = 16.

2. Complete the following table in which n is directly proportional to m.m 4 5 12 - 3.5

n 16 20 - 28 -

3. Observe the following table and determine which table represent direct variation.a)

4. m n and n=7 when m=154 find the value of m when n =14.5. When a varies directly as b3; and a = 2 when b = 1. Find the value of a when b is 3.6. y has direct proportion with x and x= 5 when y=12. Find (i) the value of y when x = 9.5, (ii)

the value of x when y = 72.

7. x y and y=16 when x=7. Find the value of y when x= 28.

X 12 5 2

Y 8 20 5

p 12 15 24

q 8 10 16

m 4 6 2

n 1/3 1/2 1/4

U 5 4 10

v 4 5 2


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4.2

1. Write the following statement by using the sign of variation.a) The electric current (I) in a circuit is directly proportional difference (V).b)

Quantity of food required varies as number of persons.

c) The area as square varies directly as the square of its diagonal.d) The mass of an iron block has direct variation with its volume.e) The number of notebooks varies as the cost of notebooks.

2. The number of paper sheet directly proportional to its weight. If the weight of 12 sheet ofpaper is 40 gm how many sheet of the paper would 2500 gm weight?

3. The number of books varies directly as the cost of books. The cost of 10 books is Rs. 150.How many such books can be purchased for Rs. 600?

4. The electric current (I) flowing through a circuit is directly proportional to the potentialdifference (V) in it. When the potential difference is 60 volts, the electric current is 1.5

amperes. Find the electric current flowing through the circuit when the potential difference is

100 volts.

5. The simple interest on a given amount at a given rate of interest varies directly as the period.The simple interest on the amount for 2 year is Rs. 150 find the simple interest for 5 year.

6. The mass of an iron block varies directly as its volume. The mass of the iron block havingvolume 250 cm

3is 2000gm. find the mass of the iron block having volume 150 cm

3.

7. The length of the piece of cloth varies directly as its cost. The cost of the cloth having length24 m is Rs. 840. Find the length of a cloth having cost Rs. 525.

8. The length of the shadow of an object of the day and its height at a particular time variesdirectly with the each other. At a particular time of the day, length of shadow of a shrub is 64

cm and height is 40 cm. find the length of a shadow when the height of a tree is 8.8 metre.


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4.3

1. Transform the following using sign of variation.a) The wave length of sound () and its frequency () are in inverse proportion.b) The electric current (I) in a circuit is inversely proportional to resistance (R).

2. Observe the following data and state which pair of variables is in inverse variation.X 100 200 300 400

Y 60 30 20 15

X 50 40 30 20

Y 10 20 05 04

A 90 60 45 30 20

B 10 15 20 25 303. y varies inversely as x and x = 6 and y = 9 .find the constant of variation and the equation of

variation.

4. (i) If x

, complete the following table.

(ii) If x


A 20 8 - -

B 4 - 5 40

(iii) If m


M

40 -

N 10 - 20 -

5. Y varies inversely as x and y = 48 when x= 5 find(i) The value of x when y = 15.(ii)

The value of y when x = 15.

6. If p and the constant of variation k = 120, find the value of p when q = 40.

7. If x varies inversely as y and x= 10 when y =8 then find y when x= 4.8. If x varies inversely as y and x= 10 when y =21 then find x when y= 7.9. If x varies inversely as y and x= 33 when y =12 then find x when y= 11.10.If x varies inversely as y and x=

when y =18 then find y when x= 4.

11.If a

and b = 4 when a = 18 find the value of a when b= 10.

X 36 12 9 -

Y

2 - 8 24


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4.4

1. The rate of the flow of water through a pipe varies inversely as the time required filling the tank.When the flow of water is 120 litres per minute, it takes 35 minutes to fill the tank. If it takes 21

minutes to fill the tank, find the rate of flow of water through the pipe.

2. The wave length of a sound and its frequency are inversely proportional to each other. If thefrequency is 280 hertz then the wavelength is 60 cm. find the frequency when the wave length is

100 cm.

3. The force of attraction between two unlike magnetic poles varies inversely as the square of thedistance between them. When the distance between two poles is 6 cm the force of attraction is 3

dynes. Find the force of attraction between the same two poles when the distance between them is

18 cm.

4. Number of children and number of sweets each child gets in inverse proportion. If sweets aredistributed equally among 30 children, each one will get 5 sweets. How many sweets would each

one gets, if the number of the children is reduced by 5?

5. The number of boxes and number bottles in each box are in inverse proportion. Batches of bottleswere packed in 25 boxes with 10 bottles in each box. If the same batch of bottles is packed using 5

bottles in each box, how many boxes would be filled?

6. Number of animal and number of days required to feed the food are in inverse proportion. Afarmer has enough food to feed 20 animals in his cattle for 8 days. How many days would the food

last if there were 20 animals more in his cattle?

7. Number of taps and time required to fill up a tank are in inverse proportion. 6 taps are required tofill a tank in 1 hour 10 minutes. How long will take if only 5 taps of the same type are used?


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4.5

1. If y is directly proportional to x and inversely proportional to z and if y = 12 when x = 6 and z = 21then find the value of y when x = 3.2 and z = 2.2.

2. X varies jointly as y and z2 and x = 18 when y = 32 and z = 2. Find he value of x when y = 2 andz = 4.

3. The weight of a solid right circular varies as the square of its diameter and its height jointly. Aright circular cone is having its diameter 5 cm, height 4 cm and weight 500 gm. What is the weight

of a solid right circular cone having 7 cm diameter and 9 cm height?

4. The area of a triangle is directly proportional to its base and corresponding height. The area of atriangle having base 8 cm and height 6 cm is 24 sq. cm. find the base of the triangle whose height

is 8 cm and area is 40 sq. cm.

5. Write down the relation of variation between the variables in the following formulae.(i)

= k (k is constant)

(ii)D =

(M is constant)

(iii)C = D ( is constant)(iv) I = k

( k is constant)


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Problem set4b

1. The pressure of wind on a plane surface varies directly to the square of its speed. When the wind isblowing with a speed of 25 km/ hr, its pressure on a plane surface is 1550 n/m

2. Find the pressure

when the wind blows at the speed of 75 km/hr.

2. Monthly expenditure of a person varies directly to his monthly income. When the expenditure isRs.3000 his monthly income is Rs. 4500. Find the monthly expenditure when his income is

Rs.15000.

3. Number of workers varies inversely as the number of days required to complete a work. If 45workers completed a work in 90 days. How many days will be required to complete the same work

by 30 workers?

4. Number of books stacked in shelf in inversely proportional to the thickness of books. In a library180 books having thickness 3 cm each can be stacked in a shelf. If the thickness is reduced to 2 cm

then how many such books can be stacked in the shelf?

5. The time required to cover the given distance is inversely proportional to the average speed of avehicle. If the speed is 45 km/hr, it takes 3 hours to cover a certain distance. Find the average

speed of vehicle if the same distance is to be covered in 2 hours.

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