# UNITARY METHOD

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.

=  16.403/47

=  0.349 kilograms

=  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. Kindly mail your feedback to v4formath@gmail.com

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