A, B and C can do a piece of work in 20, 24 and 30 days, respectively. They undertook to do the piece of work for ₹ 5400. They begin the work together but B left 2 days before the completion of work and C left 5 days before the completion of work. The share of A from the assured money is

₹ 2700
₹ 540
₹ 1800
₹ 600

Correct Answer: ₹ 2700

Explanation:

Let the number of days to complete the work be N.
According to the question,
k/20 + (k - 2)/24 + (k - 5)/ 30 = 1
⇒ [6k + 5(k - 2) + 4(k - 5)] / 120 = 1
⇒ 6k + 5k + 4k = 120 + 10 + 20
⇒ 15k = 150
∴ k = 10
∴ Work done by A = 10/20 = 1/2
∴ Share of A from the assured money
= (1/2) x 5400
= ₹ 2700

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