X and Y together can do a work in $2\frac{2}{5}$ day days. Y and Z together can do the same working 3 days, and X and Z together can do the same work in 4 days. The time taken by X, Y and Z together to do the same work is:
Answer & explanation
Correct answer: option 2
X + Y = \( {2 }_{5 }^{2 } \) days,
Y + Z = 3 days,
Z + X = 4 days,
⇒ Adding all the efficiencies,
⇒ 2(X + Y + Z)= 12,
⇒ X + Y + Z = 6,
⇒ Time taken by X + Y + Z to complete the work = \(\frac{12}{2}\) = 6 days, ..(\(\frac{Work}{Efficiency}\) = Time)