Question

A labourer is engaged for 20 days on the condition that he will receive Rs.120 for each day, he works and will be fined Rs.10 for each day he is absent. If he receives Rs.1880 in all, for how many days did he remain absent?

Answer 1

Hint: In this question let suppose that the labourer worked for x days, then he is absent for (20-x) days, then form an equation according to the condition given in the question.

Complete step-by-step answer:

Given the labourer is engaged for a total 20 days.
Let the labourer work for x days.

Then the number of days he is absent for is (20-x) days.

According to the question, he gets Rs. 120 for each day he works, so the total amount earned for working for x days is $120x$.

Also, Rs. 10 fined for being absent, so total fine for being absent for (20-x) days is $(20 - x) \times 10$.
Also, as given in the question, the total amount received by him in all is Rs.1880.
So, according to the given condition-
$
  120x - (20 - x) \times 10 = 1880 \\
  120x - 200 + 10x = 1880 \\
  130x - 200 = 1880 \\
  130x = 2080 \\
  x = 16 \\
 $

So, the number of days the labourer worked for is 16 days.

Hence, he was absent for $(20 - x)$ days which is equal to $(20 - 16) = 4$ days.

Note: Whenever this type of question appears, assume the unknown value as x and then make equations by using the condition given in the question and solve the equation to reach the solution. Here, in the solution, the no. of days the labourer worked for is assumed as x, so the no. of days he remained absent is (20-x). So, according to the given question equations are formed and solved to get the answer.