To complete a certain task, X is 40 % more efficient than Y, and Z is 40% less efficient than Y. Working together, they can complete the task in 21 days. Y and Z together worked for 35 days. The remaining work will be completed by X alone in:

5 days

Given,

X is 40 % more efficient than Y, and Z is 40% less efficient than Y.

X : Y : Z = 7 : 5 : 3 (Efficiency)

⇒ X + Y + Z can complete a task in 21 days = (7 + 5 + 3) x 21 = 315 units.  ..(Efficiency × Days = Total work)

⇒ Y + Z worked for 35 days = (5 + 3) x 35 = 280 units.

⇒ Remaining work = 315 - 280 = 35 units.

⇒ Time taken by X to complete 35 units = \(\frac{35}{7}\) = 5 days.    ..(\(\frac{Work}{Efficiency}\) = Time)