Problems on Unitary Method Using Inverse Variation | Unitary Method Inverse Variation Questions

If we were to find the ratio of one quantity to another quantity then we use the unitary method. Unitary Method can be solved using two different methods like Direct Variation, Inverse Variation. In this article, we have covered everything on Problems on Unitary Method using Inverse Variation.

Solve the various models of questions on the unitary method using inverse variation and enhance your accuracy and problem-solving skills in the exam. Master the topic of Unitary Method Inverse Variation by attempting the word problems on the unitary method using inverse variation here on a frequent basis.

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Unitary Method using Inverse Variation Questions with Solutions

I. An auto-rickshaw takes 4 hours to cover a distance of 32 km. If its speed is increased by 4 km/h, the time taken by it to cover the same distance is

Solution:

Given that,
Distance =32 km
Time =4hr
Speed =Distance/Time
=32/4
=8 km/hr
New speed =8+4=12 km/hr
The new time is taken by auto-rickshaw
36/12h=36×60/12
=180 min
=2h 30 min
Hence, The time taken by auto-rickshaw to cover the same distance is 2h 30 minutes.


II. A company undertook a software project to complete a part of a project in 8 months with a team of 400 persons. Later on, it was required to complete the project in 4 months. How many extra persons should he employ to complete the work?

Solution:

In 8 months, a part of the project can be completed by 400 persons.
In 1 month, the work can be completed by 8 × 400 = 3200 persons.
In 4 months, the work can be completed by 3200/4 = 800 persons.
Extra Persons required=800 – 400=400
Hence, the Extra persons required is 400 persons.


III. 16 workers can complete work in 42 days. How many workers will complete the same work in 24 days?

Solution:

This is a situation of inverse variation, now we solve using the unitary method.
To complete the work in 42 days, workers required = 16
To complete the work in 1 day, the worker required = (42 × 16)
To complete the work in 24 days workers required = (42 × 16)/24
=16
Therefore, to complete the work in 24 days, 16 workers are required.


IV. If 30 men can do a piece of work in 25 days, then 15 men will complete the same work in how many days?

Solution:

This is a situation of inverse variation, now we solve using the unitary method.
Given that,
30 men can do the work in =25 days.
1 man can do the work in =(30 × 25) days.
15 men can do the work in days= (30 × 25)/15
=50days
Therefore, 15 men can do the work in 50 days.


V. Ravi starts for his school at 8:05 a.m. on his bicycle. If he travels at a speed of 15 km/h, then he reaches his school late by 5 minutes but on traveling at 20 km/.h he reaches the school 10 minutes early. At what time does school start?

Solution:

Let the total distance =x km
Let the Time be taken =t min
With the speed of bicycle 15 km/hr, then he reaches by 5 min
x/15=t+5/60
x/15=t+1/12 –>(1)
With speed 20 km/hr then reaches his school 20 min early-
x/20=t-10/60
x/20=t-1/6 —>(2)
Subtracting 2 from 1, we get
x/15-x/20=1/12+1/6
4x-3x/60=1+2/12
x/60=1/4
x=15
Put x=15 in eq 1
1=t+1/12
t=1-1/12
t=11/12h
11/12*60=55 min
Timing of the school=8:05+55= 9:00 a.m.
Therefore, The school starts at 9:00 a.m.


VI. Sindhu starts at 8:00 AM by bicycle to reach school. She cycles at the speed of 16 km/hour and reaches the school at 8:15 AM. By how much should she increase the speed so that she can reach the school at 8:10 AM?

Solution:

This is a situation of inverse variation, now we solve using the unitary method.
In 15 minutes the same distance is covered at the speed of 16 km/hr.
In 1 minute the same distance is covered at the speed of (16 × 15) km/hr.
In 10 minutes the same distance is covered at the speed of (16 × 15)/10 km/hr.
Therefore, in 10 minutes the same distance is covered at the speed of 24 km/hr.


VII. A car covers a particular distance in 4 hours with a speed of 60 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:

This is a situation of inverse variation.
Because
more speed —–> less time
Given that,
Time is taken by the car to cover the particular distance = 4 hours and
Speed of the car = 60 mph
The formula to find the distance is
Distance = Time ⋅ Speed
Distance = 4 ⋅ 60 = 240 miles
If the given speed of 60 mph is increased by 20 mph, then the new speed will be 80 mph.
The formula to find the time is,
Time = Distance / Speed
Time = 240 / 80
Time = 3 hours
If the speed is increased by 20 mph, the time taken by the truck is 3 hours.


VIII. A man has enough money to buy 12 kg of apples at Rs150 per kg. How much can he buy, if the price is increased by Rs 2 per kg?

Solution :

This is a situation of inverse variation.
Because
more price —–> lesser pounds of apples
Cost of 12 kg of apples at Rs 150 per kg is= 12 ⋅ 150
= Rs 1800
So, the person has Rs1800.
If the price is increased by Rs 2 per kg, then the new price per kg is
= Rs 152
No. of pounds of apples he can buy with Rs 1800 is
= 1800 / 152
= 11.84
If the price is increased by Rs 2 per kg, the person can buy 11.84 kg of apples.


IX. If 5 men can paint a house in 12 hours, how many men will be able to paint it in 10 hours?

Solution:

This is a situation of inverse variation.
Because
fewer hours —–> more men
In 12 hours, the house can be painted by 5 men
No. of hours taken by 1 man to paint the house is
= No. of hours ⋅ No. of men
= 12 ⋅ 5= 60 hours
No. of men required to paint the house in 10 hours is
= 60 / 10
= 6 men
Therefore, 6 men will be able to paint the house in 10 hours.


X. Dev can complete a work in 7 days working 6 hours per day. If he works 3 hours per day, how many days will he take to complete the work?

Solution:

This is a situation of inverse variation.
Because
fewer hours per day —–> more days to complete the work
6 hours per day ——–> 7 days to complete the work
1 hour per day ———> 7 ⋅ 6 = 48 days
3 hours per day ———> 48 / 3 = 16 days
Dev can complete the work in 16 days working 3 hours per day.


XI. A man can type 8 pages of a book every day and complete it in 40 days. How many days will he take to complete it, if he types 16 pages every day?

Solution:

This is a situation of inverse variation.
Because
more pages per day—–> less days to complete the book
8 pages per day ——> 40 days
1 page per day ——–> 8 ⋅ 40 = 320 days
16 pages per day ——> 320 / 16 = 20 days
The man will complete the book in 20 days if he types 16 pages per day.


XII. If a builder can construct a house by using 30 people in 150 days, how many people are required to complete the work in 50 days?

Solution:

Given that,
30 people can construct a house in 150 days.
150 days —–> 30 people
1 day    ——-> (30. 150) people
50 days ——-> (30.150)/50= 90
Therefore, 90 people are required to complete the work in 50 days.


 

 

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