A and B can do a work in 9 days and 12 days respectively. If they work on alternate days starting with A, then in how many days will the work be completed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(10\displaystyle\frac{1}{4}\) days
Take the whole work as 36 units, the LCM of 9 and 12, so that each day’s work is a whole number. Working on alternate days, A and B together do a fixed amount every 2 days.
A’s work in a day: \(36\div9=4\) units
B’s work in a day: \(36\div12=3\) units
Every 2 days (A, then B): \(4+3=7\) units
In 10 days (5 such pairs): \(5\times7=35\) units, leaving 1 unit
The 11th day is A’s turn; he does 1 unit in \(\frac{1}{4}\) of a day
Total time \(=10\frac{1}{4}\) days