Study Material for PSC exams Government Jobs:How to do P.S.C questions based on Work rate concept

A repeating pattern in Maths section of P.S.C exams i s based on rate of work.
Let us take an example:

If A can do a  work in 10 days, B can do the same work in 15 days. In how many days they can TOGETHER complete the work?



Method:

First thought,


If A  can do a work in 10 days, How much of the total work will be completed in a day?

1/10  right.    Any doubt?

so, rate of work of A, or work done in a single day=1/10 of the whole work, 

Similarly rate of work of B will be    1/15.


So when they work together, the number of days they will take to complete the entire work must be less than what took when working alone.

Also as they are working together the rate of work will be a combination of their respective rate wof work.

Hence we can understand that

Rate of work of A nd B WORKING TOGETHER is SUM of their respective rate of work.


which is (1/10   +   1/15)


1/10   +  1/15   is solved by taking  a common denominator of 10, 15. Here it could be 30, 60,90,.....

Now
{(1/10)* 30   +   (1/15)*30}/30

=   {(3+2)/30}
= 5/30
=1/6


Rate of work of A nd B working together is   1/6

At this rate, how many days will it take to complete the work.

Rate of work* Number of days= complete work

1/6*number of days= 1(ie here 1 denote 6/6)
There for
number of days=6
Now
Number of days taken by A nd B together will be =  6 days




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