Question

A and B together can do a piece of work in 24 days. B and C together can do the same work in 30 days. A works for 8 days, B works for 17 days and C works for 31 days to complete the work. In how many days can C alone do the same work?

Answer 1

Answer:

(A+B+C)'s 1 day's work =

18

1

(A+B)'s 1 day's work =

24

1

(B+C)'s 1 day's work =

36

1

∴ (A+C)'s 1 day's work=(2×

18

1

)−(

24

1

+

36

1

)

⇒(

9

1

)−(

72

3+2

)

⇒(

9

1

−

72

5

)

⇒(

72

8−5

)

⇒

72

3

=

24

1

so A and C together will do the work in 24 days.