Unitary Method

Unitary Method

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the required value by multiplying the single unit value.

Let us understand this using an example:

The cost of 5 apples is Rs 40.

The cost of 1 apple is = 40 ÷ 5 = Rs 8

The cost of 9 apples = 9 x 8 = Rs 72

The unitary method forms an important part of more advanced mathematical concepts such as optimization and operations research where problem statements are converted into equations and then solved.

For example, you go to a supermarket and see two offers on the same product from 2 different shops:

·         Shop A is offering 1500 g sugar for Rs. 75

·         Shop B is offering 2 kg of sugar for Rs. 90

Which brand is the better deal? With Unitary method, your life would be made extremely simple! 

 You can find here that shop B is the better deal for you.

Let us consider some examples on unitary method:

Question 1: The cost of 6 notebooks is Rs 300. Find:

         i)         The number of notebooks that can be purchased with Rs 450.

         ii)       The cost of 7 notebooks

Solution: It is given that the cost of 6 notebooks = Rs 300. Hence the cost of 1 notebook = Rs 50. Now,

i)                    The number of notebooks that can be purchased with Rs 50 = 1.

Hence, the number of notebooks that can be purchased with Rs 450 = 450/50 = 9 notebooks

ii)                  The cost of 1 notebook = Rs 30. The cost of 7 notebooks = Rs 50 × 7 = Rs 350.

Question 2: 2 balls cost Rs 8. Find the cost of 3 balls.

Solution: Cost of 2 balls = Rs 18

               Cost of 1 ball = Rs 18 ÷ 2 = Rs 9

Cost of 3 balls = Rs 9 × 3 = Rs 27

Question 3: Cost of 1 book is Rs 120. What is the cost of 10 such books?

Solution: Cost of 1 book = Rs 120

Cost of 10 books = Rs 120 × 10

                            = Rs 1200

Question 4: 12 oranges cost Rs 60. Find the cost of 6 oranges.

Solution: Cost of 12 oranges = Rs 60

Cost of 1 orange = Rs 60 ÷ 12 = Rs 5

Cost of 6 oranges = Rs 6 × 5 = Rs 30

Question 5: Cost of 5 pens is Rs 50. What is the cost of 1 pen?

Solution: Cost of 5 pens = Rs 50

Cost of 1 pen = Rs 50 ÷ 5

                       = Rs 10

Question 6: 6 pencils cost Rs 96. How much will 2 such pencils cost?

Solution: Cost of 6 pencils = Rs 96

Cost of 1 pencil = Rs 96 ÷ 6 = Rs 16

Cost of 2 pencils = Rs 16 × 2 = Rs 32

Question 7: Cost of 10 note books is Rs 250. Find the cost of 15 note books.

Solution: Cost of 10 note books = Rs 250

Cost of 1 note book = Rs 250 ÷ 10

                                 = Rs 25

Cost of 15 note books = Rs 25 × 15

                                    = Rs 375

Question 8: Cost of 5 chocolates is Rs 35. Find the cost of 10 chocolates.

Solution: Cost of 5 chocolates= Rs 35

Cost of 1 chocolate = Rs 35 ÷ 5

                                 = Rs 7

Cost of 10 chocolates = Rs 7 × 10

                                    = Rs 70

 

Question 9: If the cost of 5 pens is Rs 50, then find the cost of 8 pens.

Solution: Cost of 5 pens = Rs 50

                                                   [Here, 5 is the total units and Rs 50 is the total value]

Cost of 1 pen = Rs 50/5 = Rs 10 [Value of 1 unit is Rs 10]

Therefore, cost of 8 pens = Rs 10 × 8 = Rs 80

                            [Multiplying the value of 1 unit with the required number of units]

Question 10: 40 people can sit in four cabs. How many people can sit in 19 such cabs?

Solution: Number of people who can sit in 4 cabs = 40 people

Number of people who can sit in 1 cab = 40 4 people = 10 people

Therefore, number of people who can sit in 19 cabs = 10 × 19 = 190 people

Question 11: If a bus consumes 9 litres of petrol to cover 162 km, find how many litres of petrol are required to cover 306 km.

Solution: For 162 km, petrol needed = 9 litres

For 1 km, petrol needed = 9/162 litres

For 306 km, petrol needed = 9/162 × 306 = 17 litres.

Hence, 17 litres of petrol are required to cover 306 km.

Question 12: The price of 52 kg of wheat is Rs 468. Find the price of 3 quintals of wheat.

Solution: Price of 52 kg of wheat = Rs 468

Price of 1 kg of wheat = Rs 468/52

Price of 3 quintals, i.e. 300 kg of wheat = Rs 468/52 × 300 = Rs 2700

Hence, the price of 3 quintals of wheat is Rs 2700.

Question 13: An army camp of 200 men has enough food for 60 days. How long will the food last if the number of men in the camp increases to 240?

Solution: More men, less days and less men, more days.

It is a case of inverse variation.

According to the question, since 200 men have enough food for 60 days.

1 man will have enough food for 60 × 200 days.

240 men will get food for 60 × 200/240 days = 50 days

Hence, 240 men will get food for 50 days.

Question 14: Heena can type 30 words per minute. How many minutes does she take to type 150 words?

Solution: Heena can type 30 words in 1 min.

She can type 1 word in 1/30 min.

She can type 150 words = 1/30 × 150 = 5 min

Question 15: A factory produces 480 cans in 12 minutes. At this rate, how many cans does it produce in 1 hour?

Solution: 13 min → 520 cans

1 min → 480 ÷ 12 = 40 cans

60 min → 40 × 60 = 2400 cans

The company produces 2400 cans in 1 hour.

Questions and Answers on Unitary Method

 

Question 1: If the cost of 4 kg of apples is Rs 480, then what will be the cost of 15 kg of apples?

Answer: Rs 1800

Question 2: A car can travel 150 km in 3 hours. How much distance can it travel in 12 hours?

Answer: 600 km

Question 3: If 5 packets can hold 45 candies, then how many candies are there in 9 such packets?

Answer: 81 candies

Question 4: The cost of 6 notebooks is Rs 300. What will be the cost of 14 such notebooks?

Answer: Rs 700

Question 5: 7 cartons can hold 84 oranges. How many oranges can 11 cartons hold?

Answer: 132 oranges

Question 6: The cost of 10 books is Rs 1200. What will be the cost of 16 such books?

Answer: Rs 1920

Question 7: One dozen eggs cost Rs 48. Find the cost of 8 eggs.

Answer: Rs 32

Question 8: The price of 12 kg of rice is Rs 360. What is the cost of 23 kg of rice?

Answer: Rs 690

Question 9: An airplane journey of 400 km costs Rs 4400. How much will a journey of 600 km cost?

Answer: Rs 6600

Question 10: A bus covers 240 km in 6 hours. How many kilometres will it cover in 14 hours?

Answer: 560 km

 

Note:

1.     If the cost of one object is given, we can find the cost of many objects by multiplying the cost of one object with the number of objects.

2.     If the cost of several objects are given, we can find the cost of one object by dividing the cost of several objects by the number of objects.