Question

A workman is paid Rs.150 for each days he works and is fined Rs.50 for each day he
is absent. In the month of 30 days he earned Rs.2100. For many days did he remain absent?

Answer 1

Hint: In this question, first we have to consider the number of days that the workman remained
absent suppose $x$. From that we have to find the number of days that the workman worked by
subtracting $x$ from 30, where the workman’s total earning days is 30. Since the payment per
working day and fine per absence are given, we have to find the difference of his total earning
and total fine for absence. Finally, we have to equate this value with the total earnings in 30 days.
After that we have to solve the expression for $x$.
Let the number of days of absence of the workman $ = x$ days.
Therefore, the total number of working days of the workman$ = 30 - x$
It is given that in 30 days the workman earnsRs.2100.
Since the workman is paid Rs.150 for per day for working and fined Rs.50 for each day for
absent.
Thus, in 30 days his total earning is $150 \times \left( {30 - x} \right) - 50 \times x$.
Now, comparing this expression with Rs.2100 and solving for $x$.
$\begin{array}{l}150 \times \left( {30 - x} \right) - 50 \times x = 2100\\ \Rightarrow 4500 - 150x
- 50x = 2100\\ \Rightarrow - 200x = - 2400\\ \Rightarrow x = \dfrac{{ - 2400}}{{ - 200}}\\
\Rightarrow x = 12\end{array}$

Hence, the number of days he remained absent $ = 12$
Note: Here we have to determine the number of days the workman remained absent. Since the
workman’s total earning in 30 days, how much he got paid for per day work and the fine per
absences are given. So using these data we can easily find the total number of days he remained
absent.