Problems Using Unitary Method | Unitary Method Questions and Answers

Are you facing difficulties in solving Problems using Unitary Method? If that is the case you don’t have to fret anymore as we are here to help you learn how to solve problems using unitary method. We have covered different models of questions framed on the topic so that you can master the topic.

The Unitary Method Examples provided include questions on finding unit value from a gross value, determining the required quantity using unit quantity, etc. Have a quick recap of the concept of the Unitary Method by answering the Word Problems on Unitary Method available here.

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Unitary Method Questions with Solutions

I. A bicycle factory produces 1428 bicycles in a week. How many bicycles will it produce in 20 days?

Solution:

Given that,
A bicycle factory produces bicycles in a week=1428
No. of bicycles produced in a day=1428/7=204 cycles
No. of bicycles produced in 20 days=204 × 20=4080
Therefore, No. of bicycles produced in 20 days is 4080.


II. 5 workers can make 80 toys in 8 days. How many workers will be required to make 100 toys in 4 days?

Solution:

5 workers can make 80 toys in 8 days.
1 worker can make 80 toys in 8 × 5 days.
1 worker can make 1 toy in (8 × 5)/100 days.
Let the number of workers required be x, then;
x workers can make 1 toy in (8 × 5)/( 80 × x) days
x workers can make 100 toys in (8 × 5 × 100)/(80 × x ) days
But the number of days given = 4
According to the problem,
(8 × 5 × 100)/(80× x ) = 4
4000/80x = 4
320x = 4000
x = 4000/320
x = 12
Therefore, 12 workers are required to make 100 toys in 4 days.


III. The weight of 75 articles is 5 kg. What is the weight of 180 such articles? How many such articles weigh 8 kg?

Solution:

The weight of 75 articles is= 5 kg
1 article will weigh= 5/75 kgs
So 180 such articles will weigh= 5/75 x 180
=12 kgs
Now, we have to find out how many such articles will weigh up to 8 kg..
If 5 kg weight is of 75 articles
Then 1 kg will be the weight of =75/5
=15
And 8 kg will be the weight of 15 x 8 articles
= 120
Hence, 120 articles will weigh up to 8 kg.


IV. The cost of 5 kgs of rice is Rs. 450. Find the cost of 40 kgs?

Solution:

Given that,
The cost of 5 kgs of rice is=Rs 450
The cost of 1 kg of rice is=450/5=90
The cost of 40 kgs of rice is=90 x 40=3600
Hence, the cost of 40 kgs of rice is Rs 3600.


V. 5 men can build the wall in 10 days. How many men will build the wall in 2 days?

Solution:

Given that,
5 men can build the wall in 10 days
We know that more men will take less time to build the wall. This is a case of inverse proportion.
In inverse proportion,
x1y1=x2y2
5 x  10=x. 2
50=2x
x=50/2=25
Therefore, 25 men will build the wall in 2 days.


VI. A, B, and C can do a piece of work in 20 days, 30 days, and 60 days respectively. At what time will they all together finish it ?

Solution:

A’s 1 day work = 1/20
B’s 1 day work = 1/30
C’s 1 day work = 1/60
(A + B + C)’s 1 day work = 1/20 + 1/30 + 1/60
L.C.M of (20, 30, 60) = 60.
Then, we have
(A + B + C)’s 1 day work = 3/60 + 2/60 + 1/60
(A + B + C)’s 1 day work = 6/60
(A + B + C)’s 1 day work = 1/10
So, A, B, and C can together finish the work in 10 days.


V. A worker is paid Rs.850 for 5 days’ work. If he works for 18 days, how much will he get?

Solution:

Given that,
A worker is paid money for 5 days’ work=Rs 850
A worker paid money for 1 day of work=850/5=170
For 18 days work=170 x 18= 3060
Hence, A worker will get money of Rs 3060.


VI. If 24 men can do a piece of work in 30 days, then in how many days will 40 men complete the same work?

Solution:

Given that,
24 men can do a piece of work in 30 days.
1 man can do the same work in 30/24 days.
Therefore, 40 men can do it in 30×40/24 days
=50 days
Hence,  40 men can do it in 50 days.


VII. A car travels 200 km in 3 hours.
(a) How long will it take to travel 900 km?
(b) How far will it travel in 7 hours?

Solution:

Given that,
A car travels 200 km in 3 hours.
(a) To travel 1 km, Time taken will be=3/200 hours
To travel 900 km, Time taken will be=3 × 900/200=13.5 hours
Hence, For traveling 900 km the time taken will be 13.5 hours.
(b) In 3 hours, the car travels = 200 km
In 1 hour, the car will travel = 200/3 km
In 7 hours, the car will travel = (200*7)/3
= 466.6 km
Therefore, In 7 hours the car will travel 466.6 km.


VIII. In a camp, there are provisions for 100 persons for 25 days. If 40 more persons join the camp, find the number of days the provision will last?

Solution:

Given that,
No. of persons in the camp=100
No. of days provisions are provided=25
No. of persons will join the camp=40
If no. of persons increase provisions decrease. So it is inversely proportional.
100 × 25=40 × x
2500=140x
x=2500/140
x=17
Hence, Provisions will last for 17 days.


IX. The annual rent of a shop is Rs 48000. Find the rent for 7 months?

Solution:

Given that,
The annual rent of a shop is= Rs 48000
Rent for 1 month=Rs 48000/12=Rs 4000
Rent for 7 months=7 ×Rs 4000=Rs 28000
Hence, Rent for 7 months is Rs 28000.


X. 15 workers harvest the crops in the field in 7 hours. How many workers will be required to do the same work in 5 hours?

Solution:
Given that,
15 workers harvest the crops in the field = 7 hours
No. of workers harvest the crops in the field in one hour=15 × 7=105
No. of workers harvest the crops in the field in 5 hours= 105/5=21
Therefore, No. of workers who harvest the crops in the field in 5 hours is 21.

XI. 3 buses carry 249 passengers. How many passengers can be carried by 7 such buses?

Solution:

Given that,
No. of passengers can be carried by 3 buses= 249
No. of passengers can be carried by1 bus=249/3=83
No. of passengers can be carried by 7 such buses=83 ×7=581
Hence, 581 passengers can be carried in 7 such buses.


XII. Rajesh can walk 120 km in 15  hours. What distance can he walk in for 4 hours?

Solution:

Given that,
No. of km Rajesh can walk in 15  hours=120 km
No. of km Rajesh can walk in one hour=120/15=8 km
In 4 hours, Rajesh can walk=8 × 4=32 km.
Hence, Rajesh can walk 32 km in 4 hours.


XIII. A train covers 680 km in 8 hours. What distance will it cover in 9 hours?

Solution:

Given that,
In 8 hours the train covers distance=680
The train covers the distance in 1hour = 680/8=85
In 9 hours the train covers distance=85 x 9=765 km
Hence, The distance covered in 9 hours is 765 km.


 

 

 

 

 

 

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