Inverse Variation

Q.

$A$ takes $6$ days less than the time taken by $B$ to finish a piece of work. If both $A$and$B$ together can finish it in $4$ days, How many days will $B$ take to finish the work?

Q.

If $8$ men can do a piece of work in $15$ days, how many men are required to do same piece of work in $10$ days?

Q.

There is a provision of food for 50 days for 1000 soldiers in a fort. How many soldiers should leave after 15 days so that the remaining food last for 40 more days?

1. 850

2. 1045

3. 875

4. 125

Q. 210 men working 12 hours a day can finish a job in 18 days. How many men are required to finish the job in 20 days working 14 hours a day?

Q. How do we identify that the question is of direct proportion or of inverse proportion ?

Q.

A factory requires 42 machines to produce a given number of articles in 56 days. How many machines would be required to produce the same number of atricles in 48 days ?

Q. If 10 boys can complete a piece of work in 5 days, then find the time required to complete the same work by 2 boys.

1. 25 days
2. 5 days
3. 10 days
4. 50 days

Q.

If two pipes function simultaneously, a reservoir will be filled in $12$ hours. One pipe fills the reservoir $10$hours faster than the other. How many hours will be taken for the second pipe to fill the reservoir?

Q. X varies inversely as the square of Y. If X = 5 when Y = 2 , then find the constant of variation.

1. 20
2. 10
3. 5
4. 15

Q. 10 men can complete a piece of work in 10 days. In how many days will 5 men complete double the work.

1. 20 days
2. 40 days
3. 60 days
4. 10 days

Q. Which of the following is an example of inverse variation?

1. Number of chocolates and their cost
2. Speed and distance travelled
3. Weight of salt and its cost
4. The number of workers and the time taken to complete the work.

Q.

Given that x and y are in inverse proportion, and $y_1$, $y_2$ are values of $y$ corresponding to the values $x_1$, $x_2$ of $x$ respectively. Which of the following is correct?

1. x₁y₂=x₂y₁

2. x₁y₁=x₂y₂

3. x₁x₂=y₁y₂

4. =

Q.

A carpenter can do a job in eight hours. His assistant can do the same job in ten hours. How long would it take them to do the job together?

Q. X varies inversely as the cube of Y. If X = 1 when Y = 2 , then find the constant of variation.

1. 1
2. 2
3. 4
4. 8

Q. 5 masons built a wall in 2 days. If the wall was to be built in a single day, then how many masons should be employed?

1. 12 masons
2. 8 masons
3. 10 masons
4. 9 masons

Q. The boxes are to be filled with apples in a heap. If 24 apples are put in a box then 27 boxes are needed. If 36 apples are filled in a box how many boxes will be needed?

1. 18
2. 8
3. 9
4. 16

Q. Shubham covers a distance at a speed of 50 km/h in 4 hours. How long will it take for him to cover the same distance if he travels at a speed of 80 km/h?

1. 150 minutes
2. 120 minutes
3. 100 minutes
4. 80 minutes

Q. A garrison of 2800 men has provision for 36 months at the rate of 396 gm per man per day. How many men should leave so that the same provisions may last for 42 months at the rate of 432gm per day?
___

Q.

In a college, there are 10 periods per day, each of 40 minutes. The principal wants to reduce the number of periods without changing the total working hours. Find the duration of each period, if the number of periods is reduced to 8.

1. 30 minutes

2. 45 minutes

3. 55 minutes

4. 50 minutes

Q. A field can be irrigated in 20 mins using 6 sprinklers. If two more sprinklers are added for the job, then how much less time will it take to irrigate that field?

1. 6 mins
2. 5 mins
3. 2 mins
4. 8 mins

Q. Which of the following is true about Direct Variation?

1. It describes a simple relationship between 2 variables.
2. xy=k
3. y=kx
4. None of the above

Q. The pressure of a vessel is inversely proportional to its temperature. If the pressure of the vessel is 5 Bar when the temperature of the vessel is 10 Kelvin.Find the pressure when the temperature of the vessel is 20 Kelvin.

1. 2.5 Bar
2. 10 Bar
3. 7.5 Bar
4. 5 Bar

Q.

Question 9

Which of the following vary inversely with each other?
(a) Speed and distance covered
(b) Distance covered and taxi fare
(c) Distance travelled and time taken
(d) Speed and time taken

Q.

Question 45

Sate weather the given statement is true or false.

When the distance is kept fixed, speed and time vary directly with each other.

Q.

A store is having a sale where all jeans are $\frac{1}{4}$off the regular price.

Find the constant of proportionality, then write an equation relating the sale price to the regular price.

How much would a pair of$\$29$ jeans cost on sale?

Q.

What is the purpose of Cross Multiplication?

Q. When A = 2, B = 4. Also, when A = 8, B = 1. What can be concluded about A and B?

1. They are directly proportional.
2. They are inversely proportional.
3. A + B = Constant
4. There is no relation between A and B.

Q.

Which of these are examples of direct proportions?
(i) Cost price to the grocery.
(ii) The time required for completing a work to the number of workers doing that work.
(iii) Distance covered to the time when speed is constant.

1. (i), (ii)

2. (i), (ii), (iii)

3. (i), (iii)

4. (ii)

Q.

If there are more than four terms in a proportion, then the rule of three is termed as ___

Q.

Which of the following is true for inverse proportion?

1. Cannot be used where commodities are used.

2. As one amount increases, another amount increases at the same rate.

3. As one amount decreases, another amount increases at the same rate

4. As one amount changes, another amount remains the same.