Question

if a and b can do a piece of work in 12 days b and c in 15 days c and a in 20 days when they work together the time required will be​

Answer 1

answer = 10 days ...

let a, b and c finish that work in x, y and z days resp.

work done by a in 1 day = 1/x

work done by b in 1 day = 1/y

work done by c in 1 day = 1/z

according to ques,

work done by a and b together in 1 day = 1/12

i.e ....... 1/x + 1/y = 1/12 .......(1)

similarly, 1/y + 1/z = 1/15 .......(2)

1/z + 1/a = 1/20 .......(3)

now, adding (1) , (2) and (3)....

2 ( 1/x + 1/y + 1/z) = (5 + 4 + 3)/60

=> 1/x + 1/y + 1/z = 1/10 ......... (4)

now,

work done by all a, b and c together in 1 day

= 1/x + 1/y + 1/z

= 1/10 ........... (from eqn (4). )

so, days required by all to finish that work = 10 days.....

.... ans ....