A, B and C can do a piece of work in 24, 30 and 40 days

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A, B and C can do a piece of work in 24, 30 and 40 days respectively. They began the work together but C left 4 days before completion of the work. In how many days was the work done ?

Let the work be completed in x days.
According to the question,
C worked for (x – 4) days

∴	x	+	x	+	x - 4	= 1
	24		30		40

⇒	5x + 4x + 3(x - 4)	= 1
	120

⇒	12x - 12	= 1
	120

⇒	12 (x - 1)	= 1
	120

⇒	x - 1	= 1 ⇒ x - 1 = 10
	10

⇒ x = 10 + 1 = 11 days