Let us say Ram completes a task in 10 days. And Lakshman takes 15 days to complete the same task. A typical question will expect us to find out the time taken when both Ram and Lakshman work together.
The first temptation is to just add the two values 10 and 15 and say 25. However, that does not make sense. If Ram alone could complete the work in 10 days, then when Lakshman helps him, it should take lesser than 10 days.
So, we have to find an alternative approach to answer this type of questions in TANCET.
When Ram and Lakshman work together the amount of work done in a day will be the sum of the work done by Ram in a day and that done by Lakshman in a day.
If Ram takes 10 days to complete a task, then he will complete 1/10th of the task in a day.
Similarly if Lakshman takes 15 days to complete a task, then he will complete 1/15th of the task in a day.
Now, if Ram and Lakshman worked together they will complete 1/10 + 1/15 of the task in a day.
Now, that translates to 5/30th or 1/6th of the task getting completed in a day.
This certainly makes sense as higher amount of work gets done when the two of them work together.
If Ram and Lakshman complete 1/6th of the work in a day, then the entire task will be over in 6 days (the reciprocal of the amount of work done by them in a day).
Now let us summarize the method to solve work time question:
1. The reciprocal of the time that the first person takes to complete a task is the amount of task completed by the first person in a day.
2. Find the amount of work done by the second person in a day in the same way.
3. Add the amount of task completed when the two of them work together. i.e., add the result of step 1 and step 2.
4. To find the amount of time that the two will take when they work together, find the reciprocal of the answer obtained in step 3.
Try this question
If 'A' can complete half the work in 12 days and 'B' can complete half the work in 18 days, how long will they take to complete the entire task if they worked
1. 30 days
2. 60 days
3. 7.2 days
4. 14.4 days
5. 21.6 days
Answers and explanation to this work time question.
Note that the same method can be adopted to solve questions on Pipes and Cisterns. You could get additional practice questions on the work time and pipes cisterns at the following link.