LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

INTRODUCTION OF UNITARY METHOD

**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.] **

** $100**

**So, price of 1 apple = -------- = $10**

** 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.**

**Ans.) **

**Explanation -**

**§ 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 ?**

**Ans.)**

**Explanation-**

**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.**

**Ans.)**

**Explanation -**

**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.) **