Theory:

Detailed explanation about inverse proportion:
Let us consider a group of social workers gathered at a place, and they planned to dig \(100\) pits to plant trees. If one person can dig one pit then, the following will be true:
 
If \(20\) person dig for one hour, they will take 10020 \(=\) 5 hours to complete.
 
If \(10\) person dig for one hour, they will take \(=\) 10010 \(=\) 10 hours to complete.
 
If \(5\) person dig for one hour, they will take \(=\) 1005 \(=\) 20 hours to complete.
Now, in this condition, are the number of person, and the number of hours to complete the work is in direct proportion?
If your answer is NO, that is correct. Because when the number of workers is increasing, the hours are decreasing accordingly at the same rate.
 
Now we say that these quantities are in inverse proportion.
Let us denote the number of social workers as \(X\) and the number of hours as \(Y\). Now observe the following table.
 
Number of Social Workers \(X\)\(20\)\(10\)\(5\)
Number of hours \(Y\)51020
 
From the table, we can observe that when the values of \(X\) decrease the corresponding values of \(Y\) increases in such way that the ratio of XY in each case has the same value which is a constant (say \(k\)).
 
Derivation:
Consider each of the value of \(X\) and the corresponding value of \(Y\). Their products are all equal say XY=100=k (\(k\) is a constant), and it can be expressed as XY=k (\(k\) is a constant).
 
If X1X2 are the values of \(X\) is corresponding to the values of Y1Y2 of \(Y\), respectively.
 
Therefore, X1Y1=X2Y2=k constant.
 
That is X1X2=Y2Y1.
 
Thus \(X\) and \(Y\) are in inverse proportion.
From the above table, we should take X1 and X2 from the values of \(X\). Similarly, take Y1 and Y2 from the values of \(Y\).
 
Number of Social Workers  \(X\)X1X2X3X4
Number of hours \(Y\)Y1Y2Y3Y4
 
From the above table, we can learn that we need at least \(3\) variables to find out the other value.
Do you know how to find out the values of Y2, Y3 andY4?
 
Step 1:
 
Let's consider that X1 and Y1 are in \(1\) series, X2 and X3 are in \(2\) series and so on.
 
If  X1, X2 and Y1 values are given using these values, we can find out Y2.
 
Step 2:
 
Similarly to find Y3 value first, you have to make sure that you know the values of  X2X3 and Y2.
 
If you don't know that you have to find out that unknown value using previous series values.
 
After that using the \(3\) variables X2, X3 and Y2, we can find out the value of  Y3.
 
Step 3:
 
Now we know the value of Y3 then using X3X4 and Y3 values we can calculate the value of Y4.