Ravi alone takes 12 days to complete a task, while Meena alone takes 24 days to complete the same task.
Consider the following statements:
I. Working together, Ravi and Meena complete the task in 18 days.
II. When they work together, Meena does half of the task.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither I nor II
One day’s work is the reciprocal of the time; when people work together, their one-day works add.
I. Working together, Ravi and Meena complete the task in 18 days. — Incorrect. 18 days is only the average of 12 and 24; working together must take less time than either alone.
One day’s work together \(=\displaystyle\frac{1}{12}+\displaystyle\frac{1}{24}=\displaystyle\frac{3}{24}=\displaystyle\frac{1}{8}\)
Time together \(=8\) days
II. When they work together, Meena does half of the task. — Incorrect. Meena works at half Ravi’s speed, so she does only one-third of the task.
Ravi’s rate : Meena’s rate \(=\displaystyle\frac{1}{12}:\displaystyle\frac{1}{24}=2:1\)
Meena’s share \(=\displaystyle\frac{1}{2+1}=\displaystyle\frac{1}{3}\) of the task