Define the Concept of Wages?
Wages are given in proportion to work done and indirectly proportional to the time taken by an individual.
\begin{align*}
i,e \ Wages\propto Work \ Done \end{align*}\begin{align*}
Wages \ \propto \dfrac {1}{Time} \end{align*}
Formulas on Wages Concepts
1. The ratio of wages and time for doing the same amount of work is \begin{align*} W_{1}:W_{2}=T_{2}:T_{1} \end{align*}
2. Let A can do a work in m days and B can do the same work in n days. If they work together and total wages is W then
\begin{align*}
Wage \ of \ A =\left( \dfrac {n}{m+n}\right) W
\end{align*}
\begin{align*} Wage \ of \ B =\left( \dfrac {m}{m+n}\right) W
\end{align*}
3. Let A, B, and C can finish the work in a time of m, n and p days respectively, and they receive the total wages W then
the ratio of their wages is \begin{align*} \left( \dfrac {1}{m}\right) :\left( \dfrac {1}{n}\right) :\left( \dfrac {1}{p}\right) \end{align*}
Let us solve an example problem on Wages Concepts.
Sweety can do a piece of work in 30 days and anu can do the same work in 45 days. When they work together and complete the task in what ratio will they receive their wages. Also, find what is the share of sweety if the amount given on total work is Rs.40000?
SOLUTION:
\begin{align*}
Work \ done \ by \ Sweety \ in \ 1 \ day =\dfrac {1}{30} . \\
Work \ done \ by \ Anu \ in \ 1 \ day =\dfrac {1}{45} . \\ \\
We \ have \ W_{1}:W_{2}=T_{2}:T_{1} \\ \\
Ratio \ of \ wages \ of \ sweety \ and \ anu \\ respectively \ is \\ \\
W_{1}:W_{2}=\dfrac {1}{30}:\dfrac {1}{45} \\ \\ = \ 45:30 \ = \ 3:2 \\ \\
\therefore \ ratio \ of \ their \ wage \\ is \ 3:2 \\ \\
Share \ of \ sweety
=\dfrac {3}{5}\times 40,000 \\ =24,000 \\ \\
Amount \ received \ by \ sweety \ after \\ completion \ of \ work \ is \ Rs 24,000.
\end{align*}
