Question

A,B and C together can do a piece of work in 8 days A alone can do it in 20 days,A and B can do it in 14 days.In how many days will A and C do the same work

Answer 1

A alone can do it in 20 days

In 1 day, A can do = 1/20 of the work
_______________________

A and B can do it in 14 days

So in 1 day, A and B can do = 1/14 of the work

in 1 day, B alone can do = 1/14 - 1/20 = (10-7)/140 = 3/140 of the work
_______________________

A,B and C together can do it in 8 days

So in 1 day, A, B, and C together can do = 1/8 of the work

To find how much A and C can do in 1 day, subtract B's one day work.

So A and C can do in 1 day = 1/8 - 3/140 = (1×35 - 3×2)/280 = (35-6)/280 = 29/280

To complete it, A and C need = 280/29 days ≈ 9.65 days

They Need 280/29 days

Answer 2

Answer:

9.66 Days

Step-by-step explanation:

1/A + 1/B + 1/C = 1/8    - eq 1

1/A = 1/20                    - eq 2

1/A + 1/B = 1/14             - eq 3

Eq 1 + E2 - Eq 3

1/A + 1/C = 1/8 + 1/20 - 1/14

= (1/280)(35 + 14 - 20)

= 29/280

280/29 days

= 9.66 days