Hello Aspirants!! Are you one of those candidates who are preparing for competitive exams? If yes, Don’t worry. We are here to help in all the possible ways we can. Know the important questions of direct variation and inverse variation problems. Go through the below sections to know the study material and step by step procedure to solve problems.

Direct Variation and Inverse Variation Examples

Question 1.

y varies directly with x. If x=3 when y=12, what is y when x=9?

A. 42

B. 36

C. 40

D. 38

Solution: B(36)

Explanation:

From the variation equation of y=kx

12=k(3)

Dividing both sides by 3

12/3=k(3)/3

4=k

Substituting the value of k=4 in the equation y=kx

y=4(9)

y=36

Question 2.

y varies inversely with x. If x = 4 when y = 48, what is the value of y when x is 8?

A. 24

B. 36

C. 48

D. 26

Solution: A (24)

Explanation:

From the variation equation of y=k/x

48/1 = k/4

k=192

Substitute the value in the equation y=k/x

y=192/8

y= 48.4/8 = 8*6*4/8 = 24

1. x=4
2. y=48

Multiplying the 1st equation by 2

and dividing the 2nd equation by 2

Therefore, x=8, y=24.

Question 3.

y varies jointly with x and z. If y=36 and when x=2 and z=3. Find the value of y when x=4 & z=6?

A. 50

B. 80

C. 134

D. 144

Solution: D(144)

Explanation:

From the given question, if x increases then y increases, and if z increases then y increases.

As given, x= 2 and z=3

Multiplying both the equations by 2

x=4 and z=6

As x and z are directly proportional to y. x and z doubles, therefore y also doubles.

Therefore, the value of y = 36

Multiplying by 4, the value is 144

y=144

Direct and Indirect Variation Study Material

Question 4.

y varies jointly with x and z. If y=36 when x=2 and z=3. Find the value of y when x=4 and z=6?

A. 14

B. 156

C. 122

D. 142

Solution: A(144)

Explanation:

From the variation equation y=kxz

36=k(2)(3)

36=6K

K=6

Substitute k value in the equation y=kxz

y=(4)(6)

y=24(6)

y=120

y=120+24

y=144

Question 5.

y varies inversely with the cube of x. If y is 108 when x is 2, find the value of y when x is 6?

A. 2

B. 3

C. 4

D. 6

Solution:

Explanation: C(4)

From the variation of the equation y=k/x²

As given in the question

1. x=2
2. y=108

Multiply the 1st equation by 3

Divide the equation by 27

Therefore, x=6, y=4

108=k/(2)<sup3

k=108(8)

k=864

y=8(108)/(6)³

y=2³(27.4)/6³

y=2³.3³.4/6³

y=6³.4/6³

Therefore, y=4

Question 6.

The price for 75 basketballs is 1143.75 rupees. Find the price of 26 basketballs?

396. 50 rupees
397. 20 rupees
398. 60 rupees
399. 40 rupees

Solution: A (396.50 rupees)

Explanation:

Let “m” be the price of 26 basketballs

As given In the question,

The price for 75 basket ball’s is 1143.775 rupees

The price for 26 basketballs is “m”

Since, the question belongs to direct variations (For less number of basketballs, the price will be less)

We can apply cross multiplication shortcut

75*m=26*1143.75

m=(26*1143.75)/75

m=396.50

Therefore, the cost of 26 balls is 396.50 rupees.

Question 7.

A book consists of 120 papers and each paper has 35 lines. How many papers will the book consists of if each paper has 24 lines per paper?

1. 150 papers
2. 175 papers
3. 200 papers
4. 120 papers

Solution: B (175 papers)

Explanation:

Let “m” be the no of required papers

As given in the question,

There are 35 lines and 120 papers in a book

There are 24 lines and m papers in a book

Since, it is an inverse variation (for fewer lines, there are more pages)

We have to apply “straight multiplication” as it is inverse variation.

120*35=m*24

(120.35)/24 = m

175 = m

Therefore, if every paper has 24 lines, the book will contain 175 pages.

Question 8.

A truck covers some distance in 3 Hours with a speed of 60 miles per hour. Consider that the speed is increased by 30 miles per hour, find the time taken to cover the same distance by the truck?

1. 4 Hours
2. 5 Hours
3. 6 Hours
4. 2 Hours

Solution: D (2 Hours)

Explanation:

If the given speed 60 mph is increased by 30 mph, then the new speed is 90 mph

Let “m” be the required time.

In 3 hours of time, the truck covers 60 mph

For m hours of time, the truck covers 90 mph

Since it is an inverse variation (for more speed it takes less time), therefore we have to apply the “straight multiplication” shortcut.

3*60 = m*90

(3*60)/90 = m

2=m

Therefore, if the speed is increased by 30mph, then the time taken by truck is 2 Hours.

Question 9.

In 36.5 weeks, Nandu raised 2,372.50 rupees for cancer research. If he works for 20 weeks, how much money he will raise?

1. 1300 rupees
2. 1400 rupees
3. 1600 rupees
4. 1100 rupees

Solution: A (1300 rupees)

Explanation:

Let “m” be the required amount of money

From the given question, for 36.5 weeks, Nandu raised 2,372.50 rupees. Suppose, for 20 weeks, Nandu raised m rupees.

Since, it is a direct variation(for less number of weeks, the amount raised will be less), we have to apply the “cross multiplication” shortcut.

36.5*m = 20*2372.50

m = (20*2372.50)/36.5

m=1300

Therefore, the money raised in 20 weeks is 1300 rupees

Question 10.

John takes 15 days to lose 30 kgs of his weight by doing 30 minutes of exercise per day. How many days will he need if continues the exercise for 1 Hour 30 minutes per day?

1. 10 Days
2. 5 Days
3. 2 Days
4. 8 Days

Solution: B (5 Days)

Explanation:

Let “m” be the required no of days.

For 15 Days, John takes 30 minutes, suppose that in John takes 90 minutes in m days

As, from the given question, it is an inverse variation (for more minutes per day, fewer days are required to reduce weight), therefore we have to apply “straight multiplication” shortcut.

15*30=m*90

(15*30)/90=m

5=m

Therefore, if John does exercise for 1 Hour 30 minutes per day, he takes 5 days to reduce 30 kilograms of weight.

Hope the Practice Test on Direct Variation and Inverse Variation, will help you to know the various models and questions asked. With the help of the given questions, you can easily score better marks. If you need any further clarifications, then you can comment us below. Moreover, stay tuned to our site to know more shortcuts.

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