Question

A ,B and C can do a work in 36, 54, 72 days.they started the work but A left 8 days before the compeletion of work. while B left 12 days before the completion of work.the no. of days c working is? ​

Answer 1

ANSWER

A does the work in 36 days.

∴ In 1 day A does

36

1

work.

B does the work in 54 days.

∴ In 1 day B does

54

1

work.

C does the work in 72 days.

∴ In 1 day C does

72

1

work.

Let the work is finished in x days.

So A works for x-8 days.

∴ A does

36

x−8

work

B works for x-12 days.

∴ B does

54

x−12

work.

C works for x days.

∴ C does

72

x

work.

The sum of their works = the whole work = 1 work.

∴

36

x−8

+

54

x−12

+

72

x

=1

⟹

216

6x−48+4x−48+3x

=1

⟹

216

13x−96

=1

⟹13x=312

⟹x=24

So the work is finished in 24 days