One smurf and one elf can build a treehouse together in two

Let's say there are 8 units of work.

1S + 1E = 4 units/hour
1S +2F = 4 units/hour
1E + 1F = 2 units/hour

Substituting values of S, E and F, we get:

S= 8/3 units, E= 4/3 units, and F= 2/3 units

So, 1S + 1E + 1F = 8 units/ (8/3 + 4/3 + 2/3 units) = 12/7

Answer (D) 12/7 hours

Answer: Option D

Please check the video for the step-by-step solution.

GMATinsight's Solution

From (I) and (III), 1s = 1e + 2f = 4f

Please explain the above line...

Given: One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two fairies in order to complete the same job in the same amount of time. If one elf and one fairy worked together, it would take them four hours to build the treehouse.

Asked: Assuming that work rates for smurfs, elves, and fairies remain constant, how many hours would it take one smurf, one elf, and one fairy, working together, to build the treehouse?


Let the number of days to complete the work by Smurf , elf and fairy be s, e & f respectively

1/s + 1/e = 1/2
1/s + 2/f = 1/2
1/e = 2/f: f= 2e
1/e + 1/f = 1/4
1/s + 2/e + 1/f = 1/s + 5/f = 1/2 + 1/4 = 3/4
3/f = 3/4 - 1/2 = 1/4: f=12: e=6
1/s = 1/2 - 1/6 = 2/6 = 1/3: s=3
1/s + 1/e + 1/f = 1/3 + 1/6 + 1/12 = (4+2+1)/12 = 7/12

One smurf, one elf, and one fairy, working together, would take 12/7 hours to build the treehouse

IMO D

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