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
6
t
h
day, find the initial number of men who had signed up for the work.

120
150
160
180
​

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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