Unitary Method and Its Use

**Category : **3rd Class

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 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.

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