19 Nov 2015

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Solving Problems on Time and Work

Problems based on Time and work are asked a number of time in Various Competition exam. So to score good we need to learn this topic in detail.

In This topic various question may be asked by the examiner. For solving problems Based on Time and Work Problem Some Formulae are used


  1. Suppose Time Taken By a Person to complete the job ' J ' be 'T' .So in order to find the work done by him in day will be reciprocal of T   i.e  J/T .   For Explanation Let a person eats 15 apples in 10 days so the apple eaten in one day will be 15/10  i.e  1.5 apple/day.

  2. Suppose a person can do a piece of work in 100 days. so we can find that the work done in one will be 1/100 or 1%.


Let us take problem based on it:

Q. A person can eat 10 apples in 20 days. Find how much time will he take to eat 15 apples?

A. As I told you earlier that if he does a work"J" in T days so in day he will do J/T job. In this question J=10 whereas T=20 so J/T comes out be 1/2. From this we get that he eats 1/2 apples in a day

1/2 apples ------  1 day.

so  1 apple--------- 2 days.

similarly we can find time taken by him in eating 15 apples i.e 30days.

This was an easy question. Now let us start our next section in which we will find time taken by 2 persons with different efficiency .

WORK DONE BY 2 PERSONS OR MORE:

Now let us solve problems based on work done by 2 person or more .when 2 person are doing a job with different efficienies i.e both are taking different number of days in completing the job i.e suppose one takes 'x' days and other takes 'y' days for completing the same job.

So work  done in 1 day by 1st person = 1/x.

and work done in 1 day by 2nd person= 1/y.

so the work done by both of them together in one day will be =1/x +1/y.

and the time taken by them for completing the job together is = xy/(x+y).

let us take a question for this.

Q. 2 friends ram and shyam can do a job independently in 15 and 30 days respectively. when both of them works together find the time taken by them?

A. Ram takes 15 days for completing the job. Shyam takes 30 days to complete the same job .

so, work done by ram in 1 day= 1/15.

and work done by shyam in 1 day= 1/30.

so the work done by them together in 1 day will be= 1/15=1/30 and time taken by them  for completing the job together will be (15x30)/45. which is equal to 10 days.

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