Worksheet on Inverse Variation includes various questions to practice. Learn how to Solve Inverse Variation Problems by checking out the Sample Problems covering different models. Practice using the Inverse Variation Worksheet as much as possible and get a good grip on the concept. Test your preparation standard using the Worksheet for Inverse Variation and plan your preparation accordingly. Improve your scores in the exam by consistently practicing from the Word Problems on Inverse Variation.

1. If 30 men can reap a field in 12 days, in how many days can 8 men reap the same field?

## Solution:

30 men – 12 days

8 men – ?

Since it is an inverse variation we need to apply the straight multiplication

30*12 = 8*m

m = (30*12)/8

= 45 days

Therefore, 8 men can reap the same field in 45 days.

2. 10 men can dig a pond in 6 days. How many men can dig it in 5 days?

## Solution:

10 men – 6 days

? – 5 days

Since it is inverse variation apply the straight multiplication

10*6 = m*5

60/5 = m

m = 12

Therefore, 12 men can dig the pond in 5 days.

3. A truck covers a particular distance in 2 hours with a speed of 40 miles per hour. If the speed is increased by 10 miles per hour, find the time taken by the truck to cover the same distance?

## Solution:

This is the case of Inverse Variation

Because More Speed Less Time

Given Speed is 40 miles if it is increased by 10 miles then Speed is 50 miles

No. of Hours Speed

2 40

m 50

2*40 = m*50

80 =50m

80/50 = m

m = 1.6 hours

The truck takes 1.6 hours to cover the same distance.

4. If y varies inversely as x, and y = 16 when x = 3, find x when y = 12?

## Solution:

let y = k/x

16 = k/3

Thus, k = 48

y = k/x

12 = 48/x

x = 48/12

x = 4

Therefore, x = 4.

5. The frequency of a vibrating guitar string varies inversely with its length. Suppose a guitar string 0.80 meters long vibrates 4 times per second. What frequency would a string 0.5 meters long have?

## Solution:

We know y = k/x

from the given data we can rearrange the equation as

f = k/l

4 = k/0.80

k = 0.80*4

=3.2

f = 3.2/l

= 3.2/0.5

= 6.4 times per second.

6. Amar takes 15 days to reduce 20 kilograms of his weight by doing 20 minutes of exercise per day. If he does exercise for 1 hour per day, how many days will he take to reduce the same weight?

## Solution:

More minutes Per Day = Less Days to Reduce Weight

Let m be the number of days to reduce weight

No. of Days No. of Minutes

15 20

m 60

Since it is Inverse Variation go with straightforward multiplication

15*20 = m*60

m = (15*20)/60

= 5 days

Therefore, Amar takes 5 days to reduce weight if he does 1 hour of exercise per day.

7. 12 taps having the same rate of flow, fill a tank in 24 minutes. If three taps go out of order, how long will the remaining taps take to fill the tank?

## Solution:

12 taps – 24 minutes

since three taps went out of order number of taps = 12 -3 =9

12 taps – 24 minutes

9 taps – ?

Therefore, applying the inverse variation shortcut we have the equation

12*24 = 9*m

(12*24)/9 = m

m = 32

Therefore, 9 taps take 32 minutes to fill the tank.

8. 60 patients in a hospital consume 1200 liters of milk in 30 days. At the same rate, how many patients will consume 1440 liters in 28 days?

## Solution:

Given, 60 patients consume 1200 lt of milk in 30 days and say x patients consume 1440 lt of milk in 28 days.

60*30/1200 = x*28/1440

1800/1200 = 28x/1440

18/12 = 28x/1440

3/2 = 28x/1440

3*1440/2*28 = x

x = 77 patients(Approx)

Therefore, 77 Patients can consume 1440 liters of milk in 28 days.