UNITARY METHOD -
Unitary Method is a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.
The word UNIT means one.
In Unitary Method —
1st Step — We find the value of one item by division.
2nd Step — We calculate the required value by multiplication.
Value of one unit X number of items.
Suppose you go the market to buy 4 apples. The shopkeeper tells you that he is selling 10 apples at $100. In this case, the apples are the "units" and the cost of oranges is the "value".
While solving a problem using the unitary method, it is important to recognize the units and values.
§ Always write the things to be calculated on the right hand side.
§ Write the things known on the left hand side.
§ In this sum, we know the number of oranges and the value of the oranges is unknown.
Price of 10 apples = $100
[Logic - Number of apple is 10, but we have to find the value of 1 where 1 < 10, so logically value of 1 apple should be less than value of 10 apples. So, to find out the value of 1 apple we have to divide the value of 10 apple by the number of apples (which is 10) staying with shop keepers.]
So, price of 1 apple = -------- = $10
[Logic - Now we have the value of 1 apple which is $10, so we have to find out the value of 4 apples, where 4 > 1. So in this condition as per the logic value of 4 apples must be bigger than value of 1 apple. So, we have multiply value of 1 apple with asking value of 4 apples.]
Now, price of 1 apple = $10
so, the price of 4 apples = $10 X 4 = $40
Please Note- For any unitary method, first we have to find out the value of 1 unit and then only we can get the value of desired or asking unit's value.
There are some more examples are given below for your better understanding -
Example.1) A shop keeper imposed $120 for 20 oranges, a buyer want to purchase 6 oranges. So now tell how much the buyer should pay to shop keeper for 6 pcs of oranges?
Ans.) Shop keeper imposed $120 for 20 units oranges mean he is selling 20 oranges by $120.
So, Value of 20 units oranges is $120.
now, the value of 1 unit orange is $120 ÷ 20 = $6 [Here 1 < 20, so, now we have to divide the value of 20 units orange by 20 units because value of 1 unit orange must be less than value of 20 units orange.]
Now, the price of 6 units orange is = $6 X 6 = $36
[Here, 6 > 1, so we will multiply the value of 1 orange by 6 units oranges, because, the value of 6 oranges must be bigger than 1 orange]
So, buyer should pay $36 for purchase of 6 oranges to shop keeper. (Ans.)
Example.2) If 15 bag contains total 300 kg rice, and if 80 kg more rice is suppose to be added then find out the total number of rice bag.
Ans.) As per the given condition, 15 no.s bag contains 300 kg rice
Then, each bag contains = 300 kg ÷ 15 = 20 kg rice
Now, if each bag contains 20 kg of rice
Then, to baggage 80 kg rice requirement of bag is = 80 ÷ 20 = 4 bag
So, we need to add more 4 rice bags
Hence we can say that to baggage 300 kg + 80 kg = 380 kg rice we required 15 + 4 = 19 pcs. Rice bags (Ans.)
Example.3) What will be the price of 7 shirts, if the price of 3 shirts is $645.
§ We know the price of 3 shirts = $645, We have to calculate the price of 7 shirts = ?? How ?
First, we have to find the price of 1 shirt (one unit).
It will be less, so we divide ($645 ÷ 3)
Ø Then we multiply the obtained value (price of one shirt) by 7 to find the price of 7 shirts.
Ø WE have to find price, so we start our statements with…
Ø Price of …..
As per the given condition, Price of 3 shirts is $645
now, the price of 1 shirt is = $645 ÷ 3 = $215
Now, the price of 7 shirts is = $215 X 7 = $1505
So, the price of 7 shirts is $1505 (Ans.)
Example.4) A train covers a distance of 476 km in 14 hours. What distance will it cover in 23 hours ?
We know distance covered in 14 hours = 476 km
Ø In 1 hour, less distance will be covered So we divide 476 ÷ 14
Ø But distance covered in 23 hours will be more, so we multiply 23 with the value obtained in one hour.
As per the given condition, said train by 14 hours cover 476 km distances
So, train by 1 hour covers 476 ÷ 14 = 34 Km
So, by 23 hours said train cover = 34 Km X 23 = 782 Km
So, train will cover 782 Km by 23 hours. (Ans.)
Example.5) The yearly fees for a school is $1800. Find the fees paid by a student in 7 months.
Yearly means for 1 year = 12 months.
Fees for 12 months = $1800
Fees for 1 month will be less, so we divide (1800 ÷ 12)
Fees for 7 months will be more, so we multiply
yearly = 12 months fees for a school is $1800
1 month fees for said school is $1800 ÷ 12 = $150
Now, 7 months fees for said school is = $150 X 7 = $1050
So, the fees of school for 7 months is $1050 (Ans.)