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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

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.
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### Questions and Answers

#### Click on the questions below to reveal the answers

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

0%

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

56.4 km per hour
44.3 km per hour
36.54 km per hour
46.3 km per hour

9 men
11 men
10 men
12 men

11 days
12 days
10 days
9 days

Rs 24450
Rs 27250
Rs 25350
Rs 26250

Rs 1000
Rs 875
Rs 925
Rs 750

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

(frac{2}{6})
(frac{4}{12})
(frac{3}{9})
(frac{1}{4})

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

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

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