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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.
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 m^{2}
Now,
the cost of carpeting ^{ }119 m^{2} 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
If the cost of 1 liter of oil is Rs 72.75, what will be the cost of 12 liter oil?
If a bus covers 277.8 km in 6 hours, find the speed of the bus in km per hour.
8 men can complete a work in 15 days. How many men are needed to complete the work in 10 days?
8 men can complete a work in 15 days. In how many days would 12 men complete the same work?
A man pays Rs 525 for income tax at the rate of Rs 2 per Rs 100. What will be his income?
How much is the income tax on Rs 15000 at the rate of 25 paisa per Rs 5?
Sunil can do a piece of work in 5 days. How much work can he do in 2 days?
Sarmila can finish a piece of work in 12 days. How much work can she finish in 4 days?
Shreya can do a piece of work in 5 days. How much work can she do in 4 days?
Kumar can finish a piece of work in 12 days. How much work can he finish in 6 days.
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