A is 50% more efficient than B. B alone can finish a piece of work in 30 days.
Consider the following statements:
I. A alone can finish the work in 20 days.
II. A and B together can finish the work in 12 days.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both I and II
Time is inversely proportional to efficiency: A’s efficiency is \(1.5\) times B’s, so A takes \(\displaystyle\frac{1}{1.5}\) of B’s time.
I. A alone can finish the work in 20 days. — Correct. A works 1.5 times as fast as B.
A’s time \(=\displaystyle\frac{30}{1.5}=20\) days
II. A and B together can finish the work in 12 days. — Correct. Their one-day works add to \(\frac{1}{12}\).
One day’s work together \(=\displaystyle\frac{1}{20}+\displaystyle\frac{1}{30}=\displaystyle\frac{3+2}{60}=\displaystyle\frac{1}{12}\)
Time together \(=12\) days