Is TIME available for the WORK?
In this article, we understand a simple approach that would help us solve time and work questions. The basic mantra we use in this article is that one day's work or the number of units a person does in one day. If a man does a work in 10 days, then his efficiency is defined as work done by him in 1 day i.e. he does 1/10th of the work every day. Now, another person, B does the same work in 15 days then he does 1/15th of the work in 1 day. Now if they both work on it together they will complete 1/10 + 1/15 = 5/30th of the work in 1 day or complete the work in 30/5 = 6 days (as Time and Efficiency are inversely proportional to each other).
The same very question or concept can be learnt with units work approach, which assumes the total work to be done as the LCM of the number of days taken by each of the persons to complete the work. Now in this case let us assume that the work consists of the LCM of 10 & 15 i.e. 30 units to be done by A & B. Now since A completes 30 units in 10 days so he completes 30/10 = 3 units of work per day. On the other hand, B completes 30 units of the work in 15 days so he completes 30/15 = 2 units per day. Now as they are doing the same work so they make 3 + 2 = 5 units per day. So 30 units will be made in 30/5 = 6 days.
The same very concept is applicable to Pipes and Cisterns in which two pipes fill/empty a tank in x & y hours respectively. Taking the above case only: say Pipe A can fill a tank in 10 hrs and Pipe B can empty a full tank in 15 hrs. Now assuming the capacity of the tank to be 30 litres, A fills 30/10 = 3 ltr in an hour and B drains 30/15 = 2 ltr. in an hour. The net inflow in the tank after one hour is 3 - 2 = 1 ltr. So, the tank will be filled in 30/1 = 30 hrs.
Example Question: Two pipes A and B can fill a cistern in 20 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off, so that the cistern may be filled in 12 minutes?
Solution: Do not try to solve this question by making an equation rather understand and apply the following process. As the cistern is to be filled in 12 minutes, pipe B can fill only 12/24 = half of the cistern in total time. This means the other half must be filled by the pipe A. Now A can fill the whole tank in 20 minutes, so half of the tank it can fill in half of 20 minutes i.e. 10 minutes. Now the pipe A is opened from the beginning, it should be turned off after 10 minutes and that is the answer.
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