Pipe & Work Question Answers

Work and Time - Quant/Math - CAT 2008

Question 4 the day: September 27, 2002

The question for the day is from the topic of Work and Time.

Two workers A and B manufactured a batch of identical parts. A worked for 2 hours and B worked for 5 hours and they did half the job. Then they worked together for another 3 hours and they had to do (1/20)th of the job. How much time does B take to complete the job, if he worked alone?

(1)

24 hours

(2)

12 hours

(3)

15 hours

(4)

30 hours

Correct Answer - (3)
 

 

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Solution:

Let 'a' hours be the time that worker A will take to complete the job. Let 'b' hours be the time that worker B takes to complete the job. When A works for 2 hours and B works for 5 hours half the job is done. i.e. 2/a + 5/b + 1/2. --- (1)

When they work together for the next three hours, 1/20th of the job is yet to be completed. They have completed half the job earlier and 1/20th is still left. So by working for 3 hours, they have completed 1 - 1/2- 1/20 = 9/20th of the job.

Therefore,  3/a + 3/b  = 9/20--- (2).

Solving for (1) and (2), we get b = 15 hours.