A and B and C do a job in 24 days and 30 days and 40 days respectively in how many ways can they finish the job if they work together
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Work done by A in 1 day = 1/24
Work done by B in 1 day = 1/30
Work done by C in 1 day = 1/40
Let x be the number of days to complete the work
Total work done = 1/24*x + 1/30*x + 1/40*(x-4)
(5x + 4x + 3x -12)/120 = 1
(12x-12) = 120
12x = 132
x = 11
One days work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10.
C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.
Work done by A and B together in the last 4 days = (4)(1/24 + 1/30) = 3/10.
Remaining work = 7/10, which was done by A, B and C in the initial number of days.
Number of days required for this initial work = 7 days.
Thus, the total number of days required = 4 + 7 = 11 days.
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