A, B and C can complete a piece of work separately in 10, 20 and 40 days, respectively. In how many days will the work be completed if A is assisted by both B and C every third day?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 58/7.
Given:
A, B, and C can complete a piece of work separately in 10, 20, and 40 days, respectively.
A is assisted by both B and C every third day to complete the work.
Total work = Efficiency (Work done per day) × Total time taken
Calculation:
LCM (10, 20, 40) = 40
Let the total work be 40 units.
Efficiency of A = 40/10 = 4 units
Efficiency of B = 40/20 = 2 units
Efficiency of C = 40/40 = 1 unit
In a set of 3 days, total work done = 4 × 2 + (4 + 2 + 1) = 15 units
In such two sets of 3 days, total work done = 15 × 2 = 30 units
For the next 2 days, total work will be done = 30 + 4 + 4 = 38 units
40-38 Now, time is taken to complete the work entirely = 3 × 2 + 2 + (40 - 38) / 4 + 2 + 1= 58/7 days
.. The work will be completed in 58/7 days.