## Note on Unitary Method and Variation

• Note
• Things to remember
• Exercise
• Quiz

#### Unitary Method

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

• Direct variation
• Inverse variation

### Direct Variation

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.

### Inverse Variation

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.

• The Unitary Method provides an alternative approach to solving problems.
• Percentages and simple percentage problems would normally precede the unitary method approach.
• Ratio calculations are an aspect of the unitary method.
.

### Very Short Questions

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

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

0%

Rs 5408
Rs 5404
Rs 5505
Rs 5808

Rs 565
Rs 555
Rs 595
Rs 355

6000 miles
6375 miles
6384 miles
6284 miles

70
60
90
80

5 liters
9 liters
8 liters
10 liters

12 men
20 men
15 men
16 men

10 people
8 people
6 people
15 people

60 days
45 days
69 days
30 days

5 hours
12hours
10 hours
8 hours

95 words
110 words
105 words
90 words

20 km
15 km
17 km
25 km

35 shirts
30 shirts
10 shirts
25 shirts

725 bottles
820 bottles
710 bottles
720 bottles

1240 words
1150 words
1140 words
2140 words

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