A can do piece of work in 4 hours.A and c together can do it in just 2 hours,while b and c together need 3 hours to finish the same work.B alone can complete the work in
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since , the work is same. so let us assume that the piece of work be '1'
A's 1 hour's work = 1 /4 units
(A + C)'s 1 hour's work = 1 / 2 units
( B + C )'s 1 hour's work = 1 / 3 units
(A + B + C )'s 1 hour's = 1 / 4 + 1 /3
=( 3 + 4 )/ 12 = 7 / 12 units
Find B's 1 hour's work :
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B's 1 hour's work
= (A + B + C)'s 1 hour's work - ( A + C)'s 1 hour's work
= (7/ 12) - (1/ 2 ) = (14 - 12 ) / 24 = 2 /24
= 1/ 12 units = work/ time
work = 1 ( same ) , time = 12 hours
therefore, B alone will complete the work in 12 hours .
Answer: required time = 12 hours
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A's 1 hour's work = 1 /4 units
(A + C)'s 1 hour's work = 1 / 2 units
( B + C )'s 1 hour's work = 1 / 3 units
(A + B + C )'s 1 hour's = 1 / 4 + 1 /3
=( 3 + 4 )/ 12 = 7 / 12 units
Find B's 1 hour's work :
-------------------------------
B's 1 hour's work
= (A + B + C)'s 1 hour's work - ( A + C)'s 1 hour's work
= (7/ 12) - (1/ 2 ) = (14 - 12 ) / 24 = 2 /24
= 1/ 12 units = work/ time
work = 1 ( same ) , time = 12 hours
therefore, B alone will complete the work in 12 hours .
Answer: required time = 12 hours
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