A, B and C can do a piece of work in 16, 32 and 48 days,

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A, B and C can do a piece of work in 16, 32 and 48 days, respectively. They all begin together. A work continuously till it is finished, C leaves the work 2 days before its completion and B leaves the work in 1 days before its complete. In what time is the work finished ?

1. 10 days
2. 20 days
3. 15 days
4. 30 days
5. None of these

Correct Option: E

Let the work be finished in N days.
Then, A's N day's work + B's (N - 1) days + work + C's (N - 2) day's work = 1
⇒ N/16 + (N - 1/32) + (N - 2/48) = 1
⇒ N/1 + N - 1/2 + N - 2/3 = 16
⇒ (6N + 3N - 3 + 2N - 4)/6 = 16
⇒ 11N - 7 = 96
⇒ 11N = 103
∴ N = 103/11 = 9⁴/₁₁ days