BTGmoderatorDC wrote: ↑

Wed Feb 10, 2021 5:14 pm

A and B are two laborers who have been given the task to build a house. A can build a house in 20 days while B can build it in 30 days. But B went rogue and instead of building the house, he starts breaking it at the same rate. If A starts the work on the 1st day and they work alternately, in how many days will the house get built? (Assume once the house gets build, they will stop working)

A. 60 days

B. 115 days

C. 120 days

D. 140140 days

E. 121 1/3 days


OA B


Source: e-GMAT

Solution:

We see that A’s rate is 1/20 and B’s rate is 1/30. Every two days, 1/20 - 1/30 = 3/60 - 2/60 = 1/60 of the house is built (notice we are subtracting 1/30 from 1/20 because B is breaking the house instead of building the house).

Since 1/60 of the house is built every two days, one might think that it will then take 2 x 20 = 120 days to build the entire house. However, remember that, once the house gets finished by A, then work will stop, and B will not have an opportunity to break it on the following day. Therefore, it will take some number less than 120 days to build the house, so 115 should be the correct answer. But let’s verify it.

Since 114/2 = 57, after 114 days, 1/60 x 57 = 57/60 = 19/20 of the house will be built and on the following day, the 115th day, 1/20 more of the house will be built by A. Therefore, by the end of the 115th day, 19/20 + 1/20 = 1 entire house will be built.

Answer: B