Question

A work can be completed by 40 workers in 40 days. If 5 workers leave every 10 days, how many days work will be completed?
(A) 55.66
(B) 56. 44
(C) 56.66
(D) 54.66

Answer 1

Hint: First of all, assume that a man can do the work 1 unit/day. The total units of work that 40 men can do in 1 day is 40 units. Calculate the total units of work that 40 men can do in 40 days. Calculate the units of work done by 40 men working for 10 days. Then, get the number of units of remaining work. After 10 days, we have 35 workers working for the next 10 days. Calculate the units of work done by 35 men working for 10 days. Then, get the number of units of remaining work. After 10 days, we have 30 workers working for the next 10 days. Calculate the units of work done by 30 men working for 10 days. Then, get the number of units of remaining work. After 10 days, we have 25 workers working for the next 10 days. Calculate the units of work done by 25 men working for 10 days. Then, get the number of units of remaining work. After 10 days, we have 20 workers working for the next 10 days. Calculate the units of work done by 20 men working for 10 days. Then, get the number of units of remaining work which is 100 units. Now, calculate the number of days required to finish 100 units of work. The total number of days = Working number of days of 40 workers + Working number of days of 35 workers + Working number of days of 30 workers + Working number of days of 25 workers + Working number of days of 20 workers + Working number of days of 15 workers. Solve it further and get the answer.

Complete step-by-step answer:
According to the question, it is given that,
The total number of men = 40 men.
The total number of days required to finish that work = 40 days.
Let a man do the work 1 unit/day.
The total units of work that 40 men can do in 1 day = 40 units.
 The total units of work that 40 men can do in 40 days = \[40\times 40=1600\,units\] .
Initially, we have 40 men and these all 40 workers will work for 10 days.
The total units of work that 40 men can do in 10 days = \[40\times 10=400\,units\] .
The numbers of units of remaining work = \[1600-400=1200\,units\] .
In the question, it is also given that 5 workers are leaving after every 10 days.
After 10 days, 5 men have left. Now, we have 35 men and these all 35 workers will work for 10 days.
The total units of work that 35 men can do in 10 days = \[35\times 10=400\,units\] .
The numbers of units of remaining work = \[1200-350=850\,units\] .
After 10 days, 5 men have left. Now, we have 35 men and these all 35 workers will work for 10 days.
The total units of work that 35 men can do in 10 days = \[35\times 10=350\,units\] .
The numbers of units of remaining work = \[1200-350=850\,units\] .
After 10 days, 5 men have left. Now, we have 30 men and these all 30 workers will work for 10 days.
The total units of work that 30 men can do in 10 days = \[30\times 10=300\,units\] .
The numbers of units of remaining work = \[850\,-300=550\,units\] .
After 10 days, 5 men have left. Now, we have 25 men and these all 25 workers will work for 10 days.
The total units of work that 25 men can do in 10 days = \[25\times 10=250\,units\] .
The numbers of units of remaining work = \[550-250=300\,units\] .
After 10 days, 5 men have left. Now, we have 20 men and these all 20 workers will work for 10 days.
The total units of work that 20 men can do in 10 days = \[20\times 10=200\,units\] .
The numbers of units of remaining work = \[30-200=100\,units\] .
After 10 days, 5 men have left. Now, we have 15 men and the remaining units of work to be done is 100 units.
The number of days that 15 men can take to finish 100 units of work = \[\dfrac{100}{15}=6.66\] days.
The total number of days = Working number of days of 40 workers + Working number of days of 35 workers + Working number of days of 30 workers + Working number of days of 25 workers + Working number of days of 20 workers + Working number of days of 15 workers.
Now, the total number of days = (10 +10 + 10 + 10 + 10 + 6.66) days. = 56.66 days.
Hence, the correct option is option (c).

Note: It is given that 40 workers are doing the work in 40 days. There is a chance of a mistake in finding out the number of days taken by 1 man to finish the work. One may write it as \[\dfrac{40}{40}=1\] day, which is wrong. To avoid this, just assume the unit of work done by 1 man in a day. In this way, we don’t need to do calculations for the number of days taken by 1 man to finish the work.