Question

A man was engaged on a job for 30 days on the condition that he would get a wage of Rs.10 for the day he works, but he has to pay a fine of Rs.2 for each day of his absence. If he gets Rs.216 at the end. He was absent for work for how many days?
\[{\text{A}}{\text{.}}\] 7 days
\[{\text{B}}{\text{.}}\] 8 days
\[{\text{C}}{\text{.}}\] 9 days
\[{\text{D}}{\text{.}}\] 10 days
\[{\text{E}}{\text{.}}\] None of these

Answer 1

Hint: In this question if x is the day a man worked then (30-x) is the absent days. Use this condition to make the required algebraic equation and solve further.

Complete step-by-step answer:
 Let he work for $x$ days then he was absent for $\left( {30 - x} \right)$ days
Total amount paid = Rs. 216
Now according to question,
$
  10 \times x - 2\left( {30 - x} \right) = 216 \\
  10x - 60 + 2x = 216 \\
  12x = 276 \\
  x = 23 \\
$
Number of working days = 23, therefore
No of absent days $ = \left( {30 - x} \right) = 30 - 23 = 7$ days
So, option A is the correct answer.

Note: In this type of algebraic world problems first we take a variable like here we took $x$ number of working days and then formed the required equation, after solving the equation we found the value of $x$, after that we put its value in the equation $\left( {30 - x} \right)$ and finally found the number of absent days.