10 Men begin to work together on a job, but after some days, 4 of them leave the job. As a result the job which could have been completed in 40 days is completed in 50 days. How many days after the commencement of the work did the 4 men leave?

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answer is A.

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Detailed Solution

Concept- Let x be the number of days after the four men left. 10 guys complete the job in 40 days, while after 4 men leave, the job takes 50 days to complete. The number of days left for 10 guys after x days is

; the number of days left for 6 men is. While six guys may complete the same task in

ten men can complete it in 40 days. In order to find the value of x, equal these two.
Ten men start working on a project together, but after a few days, four of them quit. As a result, the task that could have taken 40 days to accomplish takes 50 days.
We must ascertain how many days the four men left.
It takes 40 days to treat 10 males. However, 4 men quit after a certain number of days, and the remaining men accomplished the job in 50 days. As a result, after x days, the work completed by 10 men in

days and that of 6 men in

days are equal.
Therefore,

By extending the previous formula, we obtain

.
Putting the constant terms and terms containing x to one side, we obtain

So, after 25 days, the 4 guys quit their jobs, leaving 10 men to finish the job for another 25 days with the remaining 6 men.
Hence, the correct answer is option 1.

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