To do a certain task X would take 3 times as long as Y and Z together; and Z would takes 4 times as long as Y and X together. Three of them together can complete the task in 10 days. How much time is taken by X and Z to complete the task?
Answer & explanation
Correct answer: option 4
X + Y + Z = 10 days,
Efficiency α \(\frac{1}{Time}\)
Therefore, X : Y + Z, and Z : Y + X
Efficiency 1 : 3 1 : 4
Making addition of Efficiency equal, by multiplying (X : Y + Z) with 5 and (Z : Y + X) with 4. we get,
⇒ X : Y + Z and Z : Y + X
Efficiency 5 : 15 4 : 16
Simplifying, we get X = 5, Y = 11, Z = 4,
⇒ Total work = (5 + 11 + 4) x 10 days = 200 units ..(Efficiency × Days = Total work)
⇒ Time taken by X and Z to complete the task together = \(\frac{200}{5 +4}\) = \(\frac{200}{9}\) =\( {200 }_{ 9}^{ 2} \) days.