XAT 2020 Question 70
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XAT
Let the work done per day by X, Y and Z is respectively 'x', 'y' and 'z' units.
According to the first statement, out of 6 days, X works for 5 days, and Y works for 5 days. Total work done = 5x + 5y = 1...(i)
According to the second statement, out of 8 days, Z works for 7 days and X works for 6 days and they complete two jobs. 7z + 6x = 2... (ii)
According to the third statement, out of 12 days, Y works for 10 days and Z works for 10 days and they complete three jobs. 10y + 10z = 3...(iii)
Solving, we get x = 1/10, y = 1/10, z = 2/10.
=> every day, X does 10% of the job, Y does 10% of the job and Z does 20% of the job.
Together, every day they can do 40% of the job. Hence to complete 100% of the job, they will take 100/40 = 2.5 days.