A and B, working separately can do a piece of work in 12 days and 20 days respectively. If they work alternately, beginning with A, then in how many days, can the work be completed?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 15
When two people work on alternate days, a pair of days (one day of A, one of B) is the repeating unit.
Assuming the whole work to be 60 units (the LCM of 12 and 20):
A does \(60\div12=5\) units a day and B does \(60\div20=3\) units a day
Every pair of days (A, then B) gives \(5+3=8\) units
7 pairs, that is, 14 days, give \(7\times8=56\) units, so 4 units are left
Day 15 is A’s turn; A needs \(\frac{4}{5}\) of the day for the last 4 units
So the work ends on the 15th day, after \(14\frac{4}{5}\) days of work. The answer given by NTA, 15, counts the day on which the work is finished.