The efficiency of A is 20% more than the efficiency of B. Working together,…
2019
The efficiency of A is 20% more than the efficiency of B. Working together, they can complete a certain piece of work in 10 days. In how many days will B alone complete 50% of that work?
- A.
9 / 9
- B.
11 / 11
- C.
10 / 10
- D.
12 / 12
Attempted by 17 students.
Show answer & explanation
Correct answer: B
Step-by-Step Solution
To solve this problem, we use the relationship between efficiency, time, and total work: Total Work = Efficiency × Time.
Determine the efficiencies:
Let the efficiency of B be 1 unit per day.
Since A is 20% more efficient than B, the efficiency of A is 1 + 20% of 1 = 1.2 units per day.
Combined efficiency of A and B = 1.2 + 1 = 2.2 units per day.
Calculate the total work:
They complete the work together in 10 days.
Total Work = Combined efficiency × Time = 2.2 × 10 = 22 units.
Calculate the time for B to complete 50% of the work:
50% of the total work = 50% of 22 = 11 units.
Time taken by B alone = Work / Efficiency of B = 11 / 1 = 11 days.