Directions: Each question below is followed by two statements I and I...
Statement I
X, Y and Z together can do a piece of work in 19 days.
X and Y together can complete the work in 28.5 days
Y and Z together can complete the work in 38 days.
Total work = LCM of (19, 28.5, 38) = 114
Total Work = Efficiency × Time
114 = (X + Y + Z) × 19
⇒ (X + Y + Z) = 114 / 19 = 6 ----(1)
Similarly, 114 = (X + Y) × 28.5
⇒ (X + Y) = 114 / 28.5 = 4 ----(2)
Similarly, 114 = (Y + Z) × 38
⇒ (Y + Z) =114 / 38 = 3 ----(3)
Adding (2) and (3) and subtracting (1) from it, we get
(X + 2Y + Z) – (X + Y + Z) = (4 + 3) – 6
⇒ Y = 1
Putting in Y (3), we get
Z = 3 – 1 = 2
Now, Total Work = Efficiency × Time
⇒ 114 = Z × Time
⇒ Time = 114 / 2 = 57 days
So, statement I alone is sufficient to answer.
Statement II:
Y takes 29 days to complete the work alone.
We cannot find efficiency of Z from this statement alone.
So, statement II alone is not sufficient to answer the question.
∴ The statement I alone is sufficient to answer the question but, statement II alone is not sufficient.
Hence, the correct option is (A).