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
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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 ....
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