Question

40 men can complete a work in 40 days. They started working together. But 5 men kept on leaving the job every 10th day. In how many days will the work be completed?
$
  {\text{A}}{\text{. 45 days}} \\
  {\text{B}}{\text{. 50 days}} \\
  {\text{C}}{\text{. 55 days}} \\
  {\text{D}}{\text{. 56}}{\text{.66 days}} \\
  {\text{E}}{\text{. None of these}} \\
$

Answer 1

Hint: To compute how many days the work is going to take, we have been given two variables in the question, i.e. number of men and days, we convert the given into a single variable equation.

Complete step-by-step answer:
Given Data,
40 men can do the work in 40 days
⟹Total men days required to finish the work = 40 × 40 = 1600 men days.
Now,
According to the question, after every 10th day, 5 men leave. That means when the work began there were 40 men. After 10 days of work, there were 35 men, after another 10 days there were 30 men and so on.
⟹40 men work in 10 days = 400 men days
⟹35 men work in 10 days = 350 men days
⟹30 men work in 10 days = 300 men days
⟹25 men work in 10 days = 250 men days
⟹20 men work in 10 days = 200 men days
⟹Total men days till now = 400 + 350 + 300 + 250 + 200 = 1500 men days
⟹Rest men days = 1600 - 1500 = 100 men days
⟹Now, 15 men will work for complete 100 men days in = $\dfrac{{100}}{{15}}$ = 6.66 days
⟹So total days taken to finish the work = 10 × 5 + 6.66 = 56.66 days.
Hence, Option D is the correct answer.

Note: In order to solve this type of question the key is to compute the work done for every 10 days in a single variable form, then we repeat the process by removing 5 men every 10 days. The left over work is assigned to the men left, to obtain the duration of it, then it is added to the sum to find the total work days.