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

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Answer 2

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. ?

Solution :-

Let us assume that, initial the group has x Number of men in the job , and Each man do 1 unit of work daily.

So,

→ 1 man do in one day = 1 unit .

→ x men do in one day = x * 1 = x units.

and,

→ x men do in 5 days = 5 * x = 5x units. = Total work.

Now,

→ in first day , x men do = x units .

Second day 10 men Drop.

So,

→ in second day, (x - 10) men do = (x - 10) * 1 = (x - 10) units .

again, next day 10 more men drop .

So,

→ in third day, (x - 20) men do = (x - 20) units .

Similarly,

→ on fourth day (x - 30) men do = (x - 30) units.

→ on fifth day (x - 40) men do = (x - 40) units .

→ on last day (x - 50) men do = (x - 50) units.

Now, The work was completed .

Therefore,

→ Total work = First day work + second day + third day + fourth day + fifth day + Sixth day.

→ 5x = x + (x - 10) + (x - 20) + (x - 30) + (x - 40) + (x - 50)

→ 5x = (x + x + x + x + x + x) + (-10 - 20 - 30 - 40 - 50)

→ 5x = 6x - 150

→ 6x - 5x = 150

→ x = 150 men (Ans.)

Hence, initial there were 150 men in the group.