**Unitary Method Formula :**

In this section, we are to see the formula of unitary method and how some word problems can be solved using the formula unitary method.

The formula is,

**Unitary Method Definition and Example :**

**Definition :**

Unitary-method is all about finding value to a single unit.

Unitary-method can be used to calculate cost, measurements like liters and time.

**Example :**

If 20 apples cost $50,

then price of one apple is = 50 / 20 = $2.50

**Problem 1 :**

If 131 cans contain 838.4 liters of oil. How many liters of oil can be contained in 60 cans ?

**Solution :**

**Given :** 131 cans contain 838.4 liters of oil.

Number of liters of oil contained in one can is

= 838.4 / 131

= 6.4 liters

Then, number of liters of oil contained in 60 cans is

= 60 ⋅ 6.4

= 384 liters

**Problem 2 :**

If the total weight of 11 jack fruits is 10.56 kg, then what will be the weight of 16 jack fruits ?

**Solution :**

**Given :** Total weight of 11 jack fruits is 10.56 kg

The weight of one jack fruit is

= 10.56 / 11

= 0.96

Then, the weight of 16 jack fruit is

= 16 ⋅ 0.96

= 15.36 kilograms

**Problem 3 :**

Cost of 26 pens is $15.34. What will be cost of 12 pens ?

**Solution :**

**Given :** Cost of 26 pens is $15.34

The cost of one pen is

= 15.34 / 26

= 0.59

Then, the cost 12 pens is

= 12 ⋅ 0.59

= $7.08

**Problem 4 :**

If David's salary per year is $26,400, find his salary for four months.

**Solution :**

**Given :** David's salary per year is $26,400

We know that,

1 year = 12 months

David's salary per month is

= 26400 / 12

= $2,200

Then, David's salary for four months is

= 4 ⋅ 2200

= $8,800

**Problem 5 :**

If a car runs 150 miles in 15 liters of fuel, how many miles will it run in 10 liters of fuel ?

**Solution :**

**Given :** The car runs 150 miles in 15 liters of fuel.

No. of miles run by the car in 1 liter of fuel is

= 150 / 15

= 10 miles

Then, no. of miles run by the car in 10 liters of fuel is

= 10 ⋅ 10

= 100 miles

**Problem 6 :**

A car covers a distance of 420 miles in 3 hours. At the same rate, how much time will it take to cover 630 miles ?

**Solution :**

**Given :** The car covers a distance of 420 miles in 3 hours.

Time taken by the car to cover 1 mile

= 3 / 420 hours

Then, time taken by the car to cover 630 miles

= 630 ⋅ 3/420

= 4½ hours

**Problem 7 :**

John has earned $54,000 in the last three years. At the same rate, how much money will he earn in the next six months ?

**Solution :**

**Given :** John's has earned $54,000 in the last three years.

We know that,

1 year = 12 months

3 years = 3 ⋅ 12 = 36 months

John's earning per month is

= 54000 / 36

= 1500

Then, the money that John will earn in the next six months is

= 6 ⋅ 1500

= $9,000

**Problem 8 :**

John has earned $54,000 in the last three years. At the same rate, how much money will he earn in the next six months ?

**Solution :**

**Given :** John's has earned $54,000 in the last three years.

We know that,

1 year = 12 months

3 years = 3 ⋅ 12 = 36 months

John's earning per month is

= 54000 / 36

= 1500

Then, the money that John will earn in the next six months is

= 6 ⋅ 1500

= $9,000

**Problem 9 :**

Michael has worked for 168 hours in the last three weeks. If he had worked the same number of hours each day, how many hours would he have worked in the first 3 days ?

**Solution :**

**Given :** Michael has worked for 168 hours in 3 weeks.

We know that,

1 week = 7 days

3 weeks = 3 ⋅ 7 = 21 days

Number of hours that Michael has worked each day is

= 168 / 21

= 8 hours

Then, the number of hours that Michael has worked in the first 3 days is

= 3 ⋅ 8

= 24 hours

**Problem 10 :**

If 7 men can complete the work in 10 days working 6 hours per day, how many days will it be taken by 4 men to complete the same work working 7 hours per day ?

**Solution :**

**Given :** 7 men can complete the work in 10 days working 6 hours per day

No. of hours taken by one man to complete the work is

= No. of men ⋅ No. of days ⋅ No. of hours

= 7 ⋅ 10 ⋅ 6

= 420 hours

No. of hours taken by three men to complete the work is

= 420 / 3

= 140 hours

No. of days taken by three men to complete the work is

= Total hours / Hours per day

= 140 / 7

= 20 days

After having gone through the stuff given above, we hope that the students would have understood "Unitary method formula".

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**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

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**Converting metric units word problems**

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**Decimal representation of rational numbers**

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