Question

A group of men decided to do a job in 5 days, but 10 men kept dropping out every day. If the job was completed at the
end of the 6th day, find the initial number of men who had signed up for the work.​

Answer 1

Answer:

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Step-by-step explanation:

Let X be the initial number of men then,

According to the question,

5X = X + (X - 10) + (X - 20) + (X - 30) + (X - 40) + (X - 50)

⇒ 5X = 6X - 150

⇒ 6X - 5X = 150

⇒ X = 150 men

Answer 2

The initial number of men who had signed up for the work is 150

Step-by-step explanation:

Let the initial number of men be N

N men can do a work in 5 days

Therefore, work done by 1 man in 1 day = 1/5N

According to the question

$(N)\times\frac{1}{5N}+(N-10)\times\frac{1}{5N}+(N-20)\times\frac{1}{5N}+(N-30)\times\frac{1}{5N}+(N-40)\times\frac{1}{5N}+(N-50)\times\frac{1}{5N}=1$

$\implies \frac{1}{5N}(6N-150)=1$

$\implies 6N-150=5N$

$\implies N=150$

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