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Unitary Method

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Unitary Method

source: www.creativeakademy.org Fig: Unitary Method
source: www.creativeakademy.org
Fig: Unitary Method

It is a technique in mathematics for solving a problem finding the value of the single unit and then finding the necessary value by multiplying the single unit value. If the quantities are in direct proportion, unit value is obtained by division. Similarly, if the quantities are in inverse proportion, unit value is obtained by multiplication. For examples,

Suppose the cost of 5 pens is Rs. 50.

Then, the cost of 1 pen is Rs. \(\frac{50}{5}\) = Rs. 10

Here, 1 pen is the unit of quantity and Rs. 10 is the unit cost. The number of pens and their cost is in direct proportion.

Again, suppose 4 men can finish a work in 6 days.

Then, 1 man can finish the work in 4 × 6 days = Rs. 24 days.

Here, the number of men and their working days are in inverse proportion.

Time and Work

source: www.bankers-adda.com Fig: Time and Work
source: www.bankers-adda.com
Fig: Time and Work

In less time we do less amount of and in more time we do the greater amount of work. So, Time and amount of work done are in direct proportion. In this case, the amount of work done in unit time is obtained by division. For example,

In 8 days, Hari can do 1 work.

In 1 day, Hari can do \(\frac{1}{8}\) part of work.

\(\frac{1}{8}\) parts of work are done in 1 day.

Similarly, in 2 days, Hari can do\(\frac{2}{8}\) =\(\frac{1}{4}\) parts of the work

In 3 days, Hari can do\(\frac{3}{8}\) parts of the work.

In 4 days, Hari can do\(\frac{4}{8}\) =\(\frac{1}{2}\) parts of work and so on.



  •  If the quantities are in direct proportion, unit value is obtained by division.
  • If the quantities are in inverse proportion, unit value is obtained by multiplication. 
  •  The amount of work done in unit time is obtained by division.
.

Very Short Questions

Solution:

The cost of 12 m of clothes = Rs 600
The cost od 1 m of clothes = Rs \(\frac{600}{12}\)  
= Rs 50
The cost of 8 m of clothes = 8 × Rs 50
= Rs 400 
So, the required cost of 8 m of clothes is Rs 400.

Solution:

Here,
the length of the floor (l) = 14 m
the breadth of the floor (b) = 8.5m
∴ Area of the floor = l × b
= 14m × 8.5m
= 119 m2
Now, 
the cost of carpeting  119 m2 is 119 × Rs 75
= Rs  8925
So, the required cost of carpeting the floor is Rs 8925.

Solution:

Here, 
Rs 2 is the tax for the income of Rs 100 
Re 1 is the tax for the income of Rs \(\frac{100}{2}\) 
= Rs 50
Rs 525 is the tax for the income of Rs 525 × 50 
= Rs 26250
So, the required income of the man is Rs 26250

Solution:

Here, 
In 20 days, 7 workers build a wall
In 1 days, 20 × 7 workers build the wall
In 14 days, \(\frac{20 × 7}{14}\) workers build the wall = 10 workers build the wall 
∴ The required number of workers to be added = 10 - 7 
= 3 workers

Solution:

Here, 
In 8 days, Hari can do 1 work 
In 1 day, Hari can do \(\frac{1}{8}\) parts of the work.
In 6 days, Hari can do \(\frac{6}{8}\) parts of the work = \(\frac{3}{4}\) parts of the work.
Now,
Remaining parts of work = (1 - \(\frac{3}{4}\)) 
= \(\frac{1}{4}\) parts  of the work
So, Gopal finished \(\frac{1}{4}\) part of the work

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  • If the cost of 1 liter of oil is Rs 72.75, what will be the cost of 12 liter oil?

    Rs 835
    Rs 873
    Rs 863
    Rs 843
  • If a bus covers 277.8 km in 6 hours, find the speed of the bus in km per hour.

    46.3 km per hour
    44.3 km per hour
    36.54 km per hour
    56.4 km per hour
  • 8 men can complete a work in 15 days. How many men are needed to complete the work in 10 days?

    10 men
    9 men 
    12 men
    11 men
  • 8 men can complete a work in 15 days. In how many days would 12 men complete the same work?

    12 days
    9 days
    10 days
    11 days 
  • A man pays Rs 525 for income tax at the rate of Rs 2 per Rs 100. What will be his income?

    Rs 27250
    Rs 25350
    Rs 24450
    Rs 26250
  • How much is the income tax on Rs 15000 at the rate of 25 paisa per Rs 5?

    Rs 875
    Rs 750
    Rs 925
    Rs 1000
  • Sunil can do a piece of work in 5 days. How much work can he do in 2 days?

    (frac{1}{5})
    (frac{3}{5})
    (frac{4}{5})
    (frac{2}{5})
  • Sarmila can finish a piece of work in 12 days. How much work can she finish in 4 days?

    (frac{3}{9})
    (frac{1}{4})
    (frac{2}{6})
    (frac{4}{12})
  • Shreya can do a piece of work in 5 days. How much work can she do in 4 days?

    (frac{1}{5})
    (frac{4}{5})
    (frac{2}{5})
    (frac{3}{5})
  • Kumar can finish a piece of work in 12 days. How much work can he finish in 6 days.

    (frac{2}{6})
    (frac{1}{2})
    (frac{3}{4})
    (frac{1}{12})
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