A and B together can complete a work in 26 days. A alone can complete it in 52 days. If B works at 50 percent efficiency, then in how many days A and B together will complete the work?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 104/3 day
A alone can complete the work = 52 days
Therefore
A's daily work rate is 1/52 of the total work
given that
A and B together can complete the work = 26 days
Let's denote B's efficiency = x
Given in the question B works at 50 percent efficiency
B's work rate = 1/2 times that of A's
B's work rate = 1/2 × A's work rate = 1/2 × (1/52) = 1/104 of the total work
Now,
the combined work rate of A and B = A's work rate + B's work rate
Combined work rate = 1/52 + 1/104 = 3/104 of the total work
To find the number of days required for A and B together to complete the work, we can invert the combined work rate
Number of days = 1 / Combined work rate = 1 / (3/104) = 104/3
Therefore, A and B together will complete the work in approximately = (104/3) days