CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Time and work. It is about two people working on alternative days to complete a task. Point to ponder: If they work together, will the number of days taken decrease?

Question 13: A can complete a task in 12 days. B can complete the task in 18 days. If A and B work on this same task in alternate days starting with A, in how many days do they finish the entire task?

1. 10.8 days
2. 14.33 days
3. 11 days
4. 8.4 days

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: If they work together, will the number of days taken decrease?

A can complete a task in 12 days and B can complete the task in 18 days. So,
In one day, A can do \\frac{1}{12}\\), in one day B can do \\frac{1}{18}\\).
In two days, they can complete \\frac{1}{12}\\) + \\frac{1}{18}\\) = which is \\frac{5}{36}\\).
In 4 days, they can finish \\frac{10}{36}\\), and so on.
We can have 7 such sets of 2days each.
So, at the end of 14 days, they would have done \\frac{35}{36}\\) of task.
On the 15th day A would begin work with \\frac{1}{36}\\)of the task to finish. He can finish \\frac{1}{12}\\) in a day. So, he would take one-third of a day. So, they can finish the whole task in 14.33 days.

The question is "how many days do they finish the entire task?"

Hence, the answer is "14.33 days".

Choice B is the correct answer.