chaitanya.bhansali wrote:Mike, Mark and Matt can individually build a house in 12, 16 and 24 days respectively. If Mark starts building the house and receives help from Mike and Matt every second day, in how many days will they complete building the house?
A) 2 B) 4 C) 6 D) 8 E) 10
Let the house = 48 units.
Since Mike takes 12 days to build a house, Mike's rate = 48/12 = 4 units per day.
Since Mark takes 16 days to build a house, Mark's rate = 48/16 = 3 units per day.
Since Matt takes 24 days to build a hours, Matt's rate = 48/24 = 2 units.
When all 3 work together, their combined rate = 4+3+2 = 9 units per day.
Every 2 days:
Work produced by Mark alone on the first day = 3 units.
Work produced by all 3 on the second day = 9 units.
Thus:
Amount of work produced every 2 days = 3+9 = 12 units.
Since 12 units are produced every 2 days, the AVERAGE amount of work produced per day = 12/2 = 6 units.
At an average rate of 6 units per day, the time required to produce all 48 units = 48/6 = 8 days.
The correct answer is
D.
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