**Unitary Method Definition and Example :**

**Definition :**

This method is all about finding value to a single unit.

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

**Example :**

If 18 units of a product cost $360,

then price per unit is = 360 / 18 = $20

**Problem 1 :**

If 6 note books cost $45, then how much 8 note books costs ?

**Solution :**

**Given :** 6 note books cost $45

Cost of one note book is

= 45/6

= $7.50

Cost of 8 note books is

= 8 ⋅ 7.50

= $60

**Problem 2 :**

The fence of a hospital is to be repainted by a group of workers. If 6 workers can paint 520.2 m of the wall in an hour, then how many meters of the wall will 7 workers paint in an hour ?

**Solution :**

**Given : **6 workers can paint 520.2 m of the wall in an hour

Length of the wall can be painted by 1 worker in an hour is

= 520.2 / 6

= 86.7 meters

Length of the wall can be painted by 7 workers in an hour is

= 7 ⋅ 86.7

= 606.9 meters

**Problem 3 :**

18 mangoes cost $36. If David has $24, how many mangoes can he buy ?

**Solution :**

**Given : **18 mangoes cost $36

Cost of one mango is

= 36/18

= $2

No. of mangoes can be bought for $24 is

= 24 / Cost of 1 mango

= 24 / 2

= 12

Hence, David can buy 12 mangoes for $24.

**Problem 4 :**

A Publisher makes 3300 books in the month of November. If they make the same quantity of books every day, then how many books can they make in a leap year?

**Solution :**

**Given : **The Publisher makes 3300 books in the month of November.

In any year, the month November has 30 days.

Then, no. of books made per day is

= 3300 / 30

= 110

If an year is a leap year, then it would have 366 days.

So, no. of books can be made in a leap years is

= 366 ⋅ 110

= 40,260

**Problem 5 :**

47 baskets of mangoes weigh 16.403 kilograms. Find the weight of 18 baskets of mangoes (Round to 2 digits of decimal).

**Solution :**

**Given : **47 baskets of mangoes weigh 16.403 kilograms.

Weight of 1 basket is

= 16.403 / 47

= 0.349 kilograms

Weight of 18 baskets is

= 18 ⋅ 0.349

= 6.282

≈ 6.28 kilograms

**Problem 6 :**

We can buy 9 units of a product for $102.60. How much money do we need, if we want to buy 12 units of the same product ?

**Solution :**

**Given : **Cost of 9 units of the product is $102.60

Cost of 1 unit of the product is

= 102.60 / 9

= $11.40

Cost of 12 units of the product is

= 12 ⋅ 11.40

= $136.80

**Problem 7 :**

5 men can complete a work in 20 days working 8 hours per day. In how many hours can one man complete the same work ?

**Solution : **

**Given : **5 men can complete the work in 20 days working 8 hours per day.

Number of hours required for one man to complete the same work is

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

= 5 ⋅ 20 ⋅ 8

= 800 hours

**Problem 8 :**

8 men can complete a work in 25 days working 5 hours per day. If 5 men can complete the same work in 20 days, how many hours does each man have to work per day ?

**Solution : **

**Given : **8 men can complete the work in 25 days working 5 hours per day.

Number of hours required for one man to complete the same work is

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

= 8 ⋅ 25 ⋅ 5

= 1000 hours

If there are 5 men, then the number of hours that each man has to work to complete the work is

= 1000 / 5

= 200 hours

**Given : **The work has to be completed in 20 days.** **

So, the number of hours that each man has to work per day is

= 200 / 20

= 10 hours

Hence, 5 men can complete the same work in 20 days working 10 hours per day.

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