A and B can do a certain work in 27 days and 36 days, respectively. A worked for a few days, and then B joined him. They worked together till the completion of the work. If the work got completed in a total of 18 days, then for how many days did A and B work together?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 12.
LCM(27, 36) = 108
The efficiency of A = 108/27 = 4 units
The efficiency of B = 108/36 = 3 units
Let A work for n days
A and B worked for (18 - n) days
⇒ 4n + 7(18 - n) = 108
⇒ 4n + 126 - 7n = 108
⇒ 3n = 18
⇒ n = 6
So, A and B worked together = 18 – 6 = 12 days