3rd Class Mathematics Unitary Method Unitary Method and Its Use

           Introduction

 

Unitary method is self-indicating that this is the method for finding the value of unit article if the values of two or more articles is given. This method is widely used for the simplification of word based problems in arithmetic and geometry. In this chapter we will learn about the concept and use of unitary method.

 

          Unitary Method and Its Use

Unitary method is used for solving the problems if there are variation in the given quantity. In this method different quantities are converted into single unit and required unit is obtained by arithmetic operations. If a car travels 20 km in 15 minutes and it is required to find the distance travelled by car in 60 minutes then distance travelled by the car in 1 minute must be carried out, that is obtained by the division of  TTherefore, the distance travelled by the car in 60 minutes is    obtained by multiplying the distance travelled in 1 minute by kilometres.                                                             

 

The weight of 4 coins is 150 grams. What is the weight of 10 such coins?       

(a) 380 grams

(b) 400 grams     

(c) 500 grams

(d) 1500 grams                      

(e) None of these

 

Answer (a)

Explanation The weight of 4 coins = 150 grams therefore, the weight of 1 coin  grams i.e, the weight of 10 coins  gram.  

 

             Applications of Unitary Method

The given number of articles is converted into single unit and the value of required number of articles is obtained. The cost of 7 articles is Rs 686, for finding the cost of one article Rs 686 is divided by 7. Therefore, the cost of one article, and the cost of 12 such articles    

 

A company buys 45 computers. If the cost of total number of hard disks isB 84330, then what will be the cost of 96 such hard disks?

(a) Rs 179908

(b) Rs 179904                     

(c) Rs 179910

(d) Rs 170000                  

(e) None of these                                                

 

Answer (b)

Explanation

The cost of 45 hard disks is? 84330. Therefore, the cost off   one hard disk

The cost of 96 such hard disks

The cost of 96 such hard disk    

 

The total length of 6 equal plane figures is 54 metres. What will be the total length of 9 such plane figures?                            

(a) 82 metres

(b) 80 metres

(c) 81 metres

(d) 78 metres

(e) None of these

 

Answer (c)

Explanation The length of one figure metres.

Therefore, the length of 9 such figuresmetres.    

 

A wood cutter cuts 8 stems of trees in 18 hours. How many stems of trees are cut by him in 9 hours?

(a) 6

(b) 8

(c) 3

(d) 4

(e) None of these

 

Answer (d)

Explanation In one hour wood cutter cuts stems of trees Therefore, in 9 hours he cuts stems of trees   

 

 

 

 

      If the cost of 10 kilograms of rice is Rs 120, then what is the total cost of 560 kilograms of rice?

(a) Rs 6720

(b) Rs 9840

(c) Rs 10,000

(d) Rs 6730                                                           

(e) None of these                                                     

 

Answer (a)                                      

The cost of 10 kg of rice is Rs 120, therefore, the cost of one     kg of rice  and the cost of 560 kg of rice  

 

 

        How many computers can be bought for Rs 44000 if the cost of four computers is Rs  22000?

(a) 7

(b) 8

(c) 9

(d) 10

(e) None of these

 

Answer (b)

Explanations:

The cost of four computer sets is Rs  22000.

Hence, the cost of one computer

Thus, for Rs 44000 number of computers can be bought  

 

 

      Peter bought 3 chairs for Rs 3600 and Miriam bought the same number of chairsfor? 3900. If the cost of each chair is equal then how much more money is paid by Miriam for each chair?           

(a) Rs 80

(b) Rs 98               

(c) Rs 100

(d) Rs 60        

(e) None of these                                     

 

Answer (c)

The cost of one chair bought by Peter  the cost of one chair bought by Mariam

Hence, Rs 1300 - 1200 = Rs 100 more money is paid by Mariam for each chair.  

 

 

         Speed of a car is 60 kilometres per hour. How much distance will it travel in 10 minutes?

(a) 10

(b) 18           

(c) 12

(d) 7

(e) None of these

 

Answer (a)

Explanation

Car travels 60 km in 60 minutes.

Hence, in one minute it travels in 10 minutes car will travel kilometers.  

 

 

        A man walked 4 km in the morning in 50 minutes. There was some interruption during the walking for 10 minutes. What distance could not the cover during the interruption?

(a) 700 metres

(b) 800 metres

(c) 900 metres

(d) 1000 metres

(e) None of these

 

Answer (b)

Explantation: Distance travelled in 10 minutes metres.          

 

 

• Unitary method is used to convert the quantity in single quantity.
• The given units can be converted into its lowest unit using unitary method.
• Two different units of a same quantity can be converted into a single unit.
• If the cost of an article is in rupees and paise then it is converted into either rupees or paise.
• If length of an object is given in meters and centimeters then for solving the   measurement based problem meters and centimeters are converted into either metres or in centimeters.

 

 

• The word mathematics is derived from the Greek word mathema.
• Babylonians were developed the elementary algebra.
• Height of a pyramid using geometry was first calculated by great scientist Thales.