A and B working together; can do a piece of work in 4

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(A + B)’s 1 hour’s work =	2	.......(i)
	9

(B + C)’s 1 hour’s work =	1	.......(ii)
	3

(C + A)’s 1 hour’s work =	4	.......(iii)
	9

Adding all three equations,

2 (A + B + C)’s 1 hour’s work =	2	+	1	+	4
	9		3		9

2 (A + B + C)’s 1 hour’s work =	2 + 3 + 4	= 1
	9

∴ A, B and C together will complete the work in 2 hours.
Second method to solve this question ,
Here , x = 9 / 2 , y = 3 , z = 9 / 4

Time taken =	( 18 × 27 ) / 8
	{ ( 27/2 ) + ( 27/4 ) + ( 81/8 ) }

Time taken =	18 × 27	×	8
	8		( 108 + 54 + 81 )

Time taken =	18 × 27	= 2 hours
	243

A and B working together; can do a piece of work in 4	1	hours. B and C working together
	2

can do it in 3 hours. C and A working together can do it in 2	1	hours. All of them
	4