X, Y and E can do piece of work in 24, 30 and 40 days respectively. All three began to work together but X and Y left 6 and 8 days respectively before completion of the work. In how many days was the work completed?
X’s one day’s work = 1/24days Y’s one day’s work = 1/30days E’s one day’s work = 1/40days Then, (x - 6)/24 + (x - 8)/30 + (x)/40 = 1 (5(x-6) + 4(x-8)+3x)/120 = 1 5x – 30 + 4x – 32 + 3x = 120 12x = 120 + 62 12x = 182 x = 182/12 ∴ x = 91/6 days = 15(1/6) days
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