A is four times as good a workman as B and together they finish a piece of work in 84/15 days. In how many days can A alone finish the work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 7 days.
Given that, efficiency of A = 4 × efficiency of B
Time taken by A and B together to complete the work = 84/15 days
Let the total work to be done be 420 units.
Total work = Efficiency × Time taken
Efficiency of (A + B) = = 75 units/day ...(i)
Let the efficiency of B be x units/day.
According to the given question,
Efficiency of A = 4x units/day
Efficiency of (A + B) = x + 4x = 5x units/day ...(ii)
Comparing equations (i) and (ii),
⇒ 5x = 75
⇒ x = 15
Now, efficiency of A = 4x = 60 units/day
Time taken by A to complete the work = = 7 days
Hence A alone can complete the work in 7 days.