# Worksheet on Inverse Variation Using Unitary Method | Inverse Variation in Unitary Method Worksheets

Worksheet on Inverse Variation using Unitary Method has questions on finding the Inverse Variation using Unitary Method. Solve the problems in the Inverse Variation in Unitary Method Worksheet PDF and learn the concept well. Learn the respective formulas of inverse variation by referring to the problems available. Download the Unitary Method Inverse Variation Worksheet for free and prepare anytime and anywhere to master the concept.

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## Unitary Method Inverse Variation Worksheet

I. Raju can complete work in 5 days working 8 hours per day. If he works 10 hours per day, how many days will he take to complete the work?

Solution:
Given that,
No. of days Raju can complete work by working 8 hours per day=5 days
This is an inverse proportion because lesser hours per day-> more days to complete the work.
8 hours per day  -> 5 days to complete the work.
1 hour per day   -> 8× 5=40
10 hours per day  -> 40/10=4
Therefore, Raju can complete the work in 4 days by working 10 hours per day.

II. Alekya takes 30 days to reduce 2 kilograms of his weight by doing 30 minutes of exercise per day. If he does exercise for 1 hour 40 minutes per day, how many days will he take to reduce the same weight?

Solution:

Given that,
No. of days required to reduce 2 kilograms by doing 30 minutes exercise=30 days
Total minutes in 30 days=30 × 30=900 minutes
So 900 minutes of exercise are required to reduce 2 kilograms weight.
Also given, Alekya did exercise for 1 hour 40 minutes.
1 hour 40 minutes=100 minutes
No. of days required=900/100=9 days
Therefore, 9 days are required to reduce 2 kg by doing 1 hour 40 minutes of exercise.

III. If 7 men can complete the work in 20 hours, how many men will be able to complete the work in 10 hours?

Solution:

Given that,
In 20 hours, work is completed by 7 men.
No. of hours taken by 1 man to complete the work is
= No. of hours ⋅ No. of men
= 20 ⋅ 7
= 140 hours
No. of men required to complete the work in 10 hours is
= 140 / 10
= 14 men
Therefore, 14 men will be able to work in 10 hours.

IV. A school has 7 periods in a day such that each period is of 30 minutes. If the number of periods is reduced to 6, then how long would each period be?

Solution:

Given that,
A school has 7 periods in a day such that each period is of 30 minutes.
We know that Total time = Number of period × time of each period.
Total time = 7 × 30
Total time = 210 minutes
Also given,
The number of periods is reduced to 6.
We have to calculate the time of each period,
Total time = Number of period × time of each period.
By Substituting the values, we get
210 = 6 × time of each period
210/6 = time of each period
=35 minutes.
Therefore, the time of each period is 35 minutes.

V. 5 members in a family had enough food for 30 days after 8 days some members went to Delhi and thus the food lasted for 36 more days how many members left the Family?

Solution:

Given that,
5 members of a family had enough food for 30 days.
Let the number of members who went to Delhi be x.
After 8 days, number of members = (5 – x)
Given that food lasted for 36 more days.
Hence 5 × 22 = (5 – x) × 36
⇒ (5 – x) = 110/36=3
⇒ x = 5 – 3 = 2
Hence, 2 members left the family.

VI. Before going to sleep a man reads 7 pages of a book every day and completes it in 30 days. How many days will he take to complete reading the book, if he reads 10 pages every day?

Solution:

Given that,
A man reads 7 pages of a book every day and completes it in 30 days.
more pages per day—–> fewer days to complete the book (since it was inverse variation)
7 pages per day ——> 30 days
1 page per day ——–> 7 × 30 = 210 days
10 pages per day ——> 210 / 10 = 21 days
Therefore, the man will complete the book in 21 days if he reads 10 pages per day.

VII. 8 pipes are required to fill a tank in 1 hour 40 minutes. How long will it take if only 6 pipes of the same type are used?

Solution:

Let the desired time to fill the tank be x minutes.
8 pipes are required to fill a tank in 1 hour 40 minutes.
8 pipes -> 1 hour 40 minutes
We know that 1 hour=60 minute.
1 hour 40 minute=60+40=100 minutes.
In 100 mins a tank is filled with 8 pipes.
Lesser the number of pipes more will be the time required by it to fill the tank.
So, this is a case of inverse proportion.
Hence, 100×8=x×6
x=800/6
x=133
Thus, the time is taken to fill the tank with 6 pipes is 133 minutes or 1 hour 33 minutes.

VIII. A man has enough money to buy 10 kg of mangoes at Rs 80 per kg. How much can he buy, if the price is increased by Rs 2.50 per kg?

Solution:

This is a situation of inverse proportion.
more price -> less kg of apples
Given that, The cost of 10 kg of apples at Rs 80 per kg is
= 10 ⋅ 80
= Rs 800
So, the person has Rs 800.
If the price is increased by Rs 2.50 per kg, then the new price per kg is
= Rs 82.50
No. of pounds of apples he can buy with Rs 82.50 is
= 800 / 82.50
= 9.69 kg
If the price is increased by Rs 2.50 per kg, the person can buy 9.69 kg of apples.

IX. A car covers a particular distance in 4 hours with a speed of 80 miles per hour. If the speed is increased by 20 miles per hour, find the time taken by the car to cover the same distance?

Solution:

Speed, time are inversely proportional.
Given that,
Time = 4 hours and Speed = 80 mph
We know that Distance = Time ⋅ Speed
Distance = 4 ⋅ 80 = 320 miles
If the given speed of 80 mph is increased by 20 mph, then the new speed will be 100 mph.
The formula to find the time is,
Time = Distance / Speed
Time = 320 / 100
Time = 3.2 hours
The time taken by the car is 3.2 hours, when the speed is increased by 20 mph.

X.In a camp, there is food provision for 100 persons for 40 days. If 20 more persons join the camp, for how
many days will the provision last?

Solution :
More the persons, the sooner would be the provision exhausted.
So, this is a case of inverse proportion.
Let the required number of days be x.
Hence, 100 × 40=(100+20) × x
100 × 40=120 × x
x=100 × 40/120
x=33
Therefore, Provisions will be last for 33 days.

XI. A car is travelling 20 km in one hour. Find the distance traveled by car in 15 minutes?

Solution:

We know that 1 hour = 60 min
In 60 min car travels =20 km
In 1 min car will travel =20/60
In 12 min car will travel = 20/60 ×15=5 km
Therefore, the car travels 5 km in 12 minutes.

XII. If Kalpana walks 120 steps to cover a distance of 200 meters, find the distance traveled in 380 steps?

Solution:

Given that,
120 steps cover a distance of 200 meters.
1 step covers=200/120=10/6=5/3
380 steps cover a distance=380 × 5/3
=633 meters
Therefore, 380 steps cover a distance of 633 meters.