Question : X, Y, and Z can complete a work in 5 days, 15 days, and 30 days, respectively. In how many days can the work be completed if X is assisted by Y and Z together every second day?
Option 1: 5 days
Option 2: 4 days
Option 3: 7 days
Option 4: 6 days
Correct Answer: 4 days
Solution :
X, Y, and Z can complete a work in 5 days, 15 days, and 30 days, respectively
Let the total work = LCM (5, 15, 30) = 30 Units.
Efficiency of X = $\frac{30}5 = 6$ units/day
Efficiency of Y = $\frac{30}{15} = 2$ units/day
Efficiency of Z = $\frac{30}{30} = 1$ units/day
Amount of work to be done in two days = work done by X alone on day 1 + work done by X, Y, and Z together on day 2
= $6+6+2+1$
= $15$ units
So, 30 units of work be completed in 4 days.
Hence, the correct answer is 4 days.
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