Question

A labourer is engaged for 20 days on the condition that he will receive Rs 60 for each day he works and he will be fined Rs 5 for each day he is absent. If he receives Rs 745 in all, for how many days he remained absent?

Answer 1

Hint: We will add Rs 60 for every day the labourer goes to work. We will subtract Rs 5 for each day the labourer is absent. The total number of days the labourer is engaged is 20. Using this information, we will form two equations in two unknowns. We will solve the system of linear equations and obtain the required answer.

Complete step by step answer:
Let the number of days that the labourers goes to work be $x$ and the number of days he is absent from work be $y$. The labourer is engaged for 20 days. So, we get the first equation as
$x+y=20....(i)$
The total wage received by the labourer is Rs 745. He receives Rs 60 for each day he works. So, for working these days, he gets Rs $60x$. He is fined Rs 5 for each day he is absent. So, he has to pay a fine of Rs $5y$. So, we get the second equation as
$60x-5y=745....(ii)$
We have a system of linear equations and we will use the method of substitution to solve them. From equation $(i)$, we can substitute $x=20-y$ in equation $(ii)$ in the following manner,
$60\left( 20-y \right)-5y=745$
Simplifying the above equation and solving for $y$, we get
$\begin{align}
  & 1200-60y-5y=745 \\
 & \Rightarrow 1200-745=60y+5y \\
 & \Rightarrow 455=65y \\
 & \Rightarrow y=\dfrac{455}{65} \\
 & \therefore y=7 \\
\end{align}$
Substituting the value of $y=7$ in equation $(i)$, we get
$\begin{align}
  & x+7=20 \\
 & \therefore x=13 \\
\end{align}$

Hence, the number of days the labourer was absent is 7.

Note: There are other methods to solve a system of linear equations. We can solve it by Gauss elimination method, by graphing or by substitution. We should choose the method according to our convenience. The calculations should be done explicitly to avoid making any minor mistakes so that we can obtain the correct answer.