At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?

At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?

1. 24
2. 18
3. 12
4. 36

Answer and Explanation

Let the work be LCM of (9 and 12) = 36 units.

Let the amount of work done in one day with their normal efficiencies by A and B be x and y units respectively.

Therefore, (x+y)×12=36

Or x+y =3 … (1)

Similarly,

(x/2+3y)×9=36

Or x/2 +3y = 4 … (2)

Solving (1) and (2) for x, we get x =2 units

Hence, A alone would take 36/x = 36/2 = 18 days to complete the work with her normal efficiency.