The unitary method is a method, in which the value of a quantity is first obtained to find the value of any required quantity.
There are two types of variation while solving the problem of unitary method. They are
When the increase or decrease in the value of one quantity causes the increase or decrease in the value of other quantity than they are said to be direct variation. For example, the cost of goods varies directly to the numbers of goods. More good, more cost. Less good, less cost.
When the increase or decrease in the value of one quantity causes the decrease or increase in the value of other quantity then they are said to be inverse variation. For example, time and work. More time consumes to complete a piece of work with less number of men's.
Solution:
12 men can make a furniture in 9 days.
1man can make it in 9 × 12 days = 108 days.
18 men can make the furniture in \(\frac{108}{18}\) days = 6 days
Solution:
Since 6 pens cost = Rs 450.
So, cost of 1 pens = Rs \(\frac{450}{6}\) = Rs 75
So, cost of 8 pens = Rs 75×8 = Rs 600
Solution:
10 Japanese Yen = Rs 6.60
1 Japanese Yen = Rs \(\frac{6.60}{10}\)
65,300 Japanese Yen = Rs \(\frac{6.60}{10}\)× 65300 = Rs 43,098
Solution:
10 Kg Oranges cost Rs 750
1 kg Orange cost Rs \(\frac{750}{10}\) = Rs 75
6 kg Oranges cost Rs 75×6 = Rs 450
∴ 6 kg Oranges cost Rs 450
10 Workers can do the work in 18 days. How many workers are required to do the same work in 15 days?
Solution:
18 days is required to complete the work for 10 workers.
1 day is required to complete the same work for = 10×18 = 180 workers.
15 days is required to complete the work = \(\frac{180}{15}\) = 12 workers.
∴ 12 workers can do the same work in 15 days.
Solution:
Since, cost of 4 Computer chairs = Rs 1,544
So, cost of 1 Computer chairs = Rs \(\frac{1544}{4}\) = Rs 386
And cost of 14 Computer Chairs = Rs 386×14 = Rs 5,404
Solution:
In 10 days, a worker earns = Rs 1,850
In 1 day, a worker earns = Rs \(\frac{1850}{10}\) = Rs 185
In 3 days, a worker earns = Rs 185× 3 = Rs 555
Hence, he will earn Rs 555 in 3 days.
Solution:
Cost of 93m cloth = Rs 1395
Cost of 1m cloth = Rs \(\frac{1395}{93}\) Rs 15
Cost of 105m cloth = Rs 15×105 = Rs 1575
∴ The Cost of 105m cloth is Rs 1575
Solution:
If, 6 hours is required to finish the work for 4 men
1 hour is required to finish the work for 4×6 = 24 men
4 hours is required to finish the work for \(\frac{24}{4}\) = 6 men
∴ 6 men is required to finish the work in 4 hours.
Solution:
5 Euro = Rs 625
1 Euro = Rs \(\frac{625}{5}\) = Rs 125
Rs 8,946 = \(\frac{8,946}{125}\) = 71.568 Euro
Solution:
Since, Cost of 5 computer mouse = Rs1250.
So, Cost of 1 computer mouse = Rs \(\frac{1250}{5}\) = Rs 250
And Cost of 10 computer mouse = Rs 250×10 = Rs 2,500
∴ The cost of 10 computer mouse is Rs 2,500
4 computer chairs cost Rs 1544, find the cost of 14 computer chairs.
A workers earns Rs 1850 in 10 days. How much he will earn in 3 days?
If Sabina can travel 190 miles in 5 hours, how many miles she can travel for 7 days?
If 3 dozen bananas cost Rs 90, how many bananas can be bought for Rs 225 ?
If a car covers 48 km in 1 ltr of petrol, how many liters of petrol are required to cover a distance of 432 km?
12 men dig a pond in 8 days. How many men can dig it in 6 days?
4 people can finish a piece of work in 6 hours. How many can do it in 4 hours?
If 36 men can do a piece of work in 25 days, in how many days can 15 men do it?
A student working 8 hours a day takes 5 days to complete a project. How many hours a day must he work to complete it in 4 days?
Sunita types 450 words in half an hour. How words would she type in 7 minutes?
A train is moving at a uniform speed of 68 km per hour. How far will it go in 15 minutes?
12 tailors can stitch 15 shirts in a day. How many shirts will be stitched by 28 tailors in a day?
In 8 hours, workers fill 960 bottles of cold drinks. How many bottles will be filled in 6 hours.
Sanjay types 57 words in 3 minutes. How many words would he type in 1 hour?
The weight of 56 books is 7 kg. What is the weight of 90 such books?
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