Theory:

A group of people work together, and they get a share of money for the work they do is called as sharing the money for the work.
If \(A\) and \(B\) do work in \(x\) and \(y\) days, respectively, then the ratio of the work done by \(A\) and \(B\) is equal to the ratio of their wages. That is, \(\frac{1}{x} : \frac{1}{y} = y : x\)
If \(A\), \(B\) and \(C\) do the same work in \(x\), \(y\) and \(z\) days, respectively, their share of money is calculated in the ratio \(\frac{1}{x}:\frac{1}{y}:\frac{1}{z}\).
Example:
If \(A\) can finish a work in \(10\) days, \(B\) can finish a work in \(15\) days, and \(C\) can finish a work in \(20\) days. All three worked together and earned a salary of \(₹6500\). Find the amount of money earned by \(A\), \(B\) and \(C\).
 
Solution:
 
Given:
 
\(A\) can finish a work in \(10\) days.
 
\(B\) can finish a work in \(15\) days.
 
\(C\) can finish a work in \(20\) days.
The ratio of the work done by \(A\), \(B\) and \(C\) is equal to the ratio of their wages.
Thus, we have:
 
\(\frac{1}{10} : \frac{1}{15} : \frac{1}{20} =\) \(\frac{6}{60} : \frac{4}{60} : \frac{3}{60}\)
 
\(= 6 : 4 : 3\)
 
The total parts \(= 6 + 4 + 3 = 13\)
 
\(A\)'s share \(= \frac{6}{13} \times 6500 = ₹3000\)
 
\(B\)'s share \(= \frac{4}{13} \times 6500 = ₹2000\)
 
\(C\)'s share \(= \frac{3}{13} \times 6500 = ₹1500\)
 
Therefore, the shares of \(A\), \(B\) and \(C\) are \(₹3000\), \(₹2000\) and \(₹1500\) respectively.