Rashmi can do a piece of work in 16 days. Ravina can do the same work in 12 4/ 5 days, while Gitika can do it in 32 days. All of them started to work together but Rashmi leaves after 4 days. Ravina leaves the job 3 days before the completion of the work. How long would the work last?

9 days
6 days
18 days
5 days

Correct Answer: 9 days

Explanation:

Let the work lasted for N days,
Then, Rashmi's 4 day's work + Ravina (N - 3) day's + Gitika's N day's work = 1
⇒ (4/16) + (N - 3) / (12⁴/₅) + N/32 = 1
⇒ 5(N - 3)/64 + N/32 = 1 - 1/4
⇒ [5(N - 3) + 2N] / 64 = 3/4
⇒ 7N - 15 = 48
∴ N= (48 + 15)/7 = 63/7 = 9 days

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