Arun and Veer together take 18 days to do a work, while Arun and Chiru together take 30 days to do the same work. Veer is 200% more efficient than Chiru. What is the time taken by all three together to complete the work?

12 days
20 days
16 days
15 days

Correct answer: 15 days

Solution

Let Chiru's rate be $c$, so Veer's rate is $3c$. Then Arun + Chiru = $1/30$ and Arun + Veer = $1/18$. Subtracting gives $2c = 1/18 - 1/30 = 1/45$, so $c = 1/90$. Therefore, total rate = $a+c+3c = a+4c = 1/30 + 3c = 1/30 + 1/30 = 1/15$, so time = 15 days.

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