A alone can complete a work in 16 days and B alone can complete the work in 12 days. How many days will it take to complete the work if they work on alternate days starting from A.

14 days

Step-by-step explanation:

1. Convert the amount of work person A and B can do respectively in one day into fractions.

A = 1/16 B = 1/12

2. Get both fractions to a common denominator using the least common multiple. This is 48.

1/16 * 3 = 3/48 1/12 * 4 = 4/48

3. Add both fractions to find out how much work will be done in two days. We are doing this because we are working in a pattern, and this will allow us to multiply, which is more time efficient than repeatedly adding 3 and then 4.

3/48 + 4/48 = 7/48

4. Figure out how many sets of two days work (7/48) will get them to 48/48 (100% done) or closest to it without being under. This would be 7 sets.

7/48 * 7 = 49/48

5. Multiply 7 by 2. We are doing this because we worked in sets of two days to account for A working and then B, since they are taking turns.

7 * 2 = 14

6. It will take them 14 days.