The question below is followed by two statements numbered I and II. Choose the option that describes whether the statements are sufficient to answer the question.
Who among Arun, Bhargav and Chadda is the most efficient?
I. To complete a work, Chadda takes 5 times as much time as Arun and Bhargav take working together.
II. To complete a work, Arun takes as much time as Bhargav and Chadda take working together.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → The question can be answered by using one of the statements alone, but not by using the other statement alone.
Efficiency is the work done in one day. Taking the same time as two people together means doing as much work per day as both of them together. Let Arun, Bhargav and Chadda do \( a \), \( b \) and \( c \) units of work per day.
Statement I alone:
Chadda takes 5 times the time of Arun and Bhargav together, so \( c = \displaystyle\frac{a+b}{5} \)
Chadda is slower than the pair, but Arun and Bhargav are not compared: for example \( a = 3, b = 2 \) makes Arun the most efficient and \( a = 2, b = 3 \) makes Bhargav the most efficient: not sufficient
Statement II alone:
Arun alone takes as long as Bhargav and Chadda together, so \( a = b + c \)
Since \( b \) and \( c \) are both positive, \( a > b \) and \( a > c \)
So Arun is the most efficient: sufficient
Statement II alone answers the question, and statement I alone does not.