WORK AND TIME SHORTCUTS – RULE OF FRACTION

In our earlier post we have already discussed how to solve work and time problems in a matter of seconds, if you missed it, can read it here WORK AND TIME SHORTCUTS. But there are few work and time based questions where it is difficult to apply those formulae. So, in order to solve such work and time based problems we use ‘Rule of Fraction’.

What is Rule of Fraction?

It states that

1. If the required value of an item is greater than the given value of the same item then out of all the given values of other item we put the greater value as numerator and lesser value as denominator.
   
2. If the required value of an item is smaller than the given value of the same item then out of all the given values of other item we put smaller value as numerator and greater value as denominator.
   

Lets us take few examples to understand how to use the rule of fraction:

Example 1: 16 men can do a piece of work in 10 days. How many men are needed to complete the work in 40 days.

Solution:

Step 1: We have to find number of men, so write the number of given number of men (i.e; 16) first.

Step 2: Number of days increases from 10 to 40, obviously we will require less men to do the work . hence our fraction would be 10/40 and not 40/10.

Step 3: Multiply the values obtained from step 1 and step 2.

Example 2: If 30 men working 7 hrs. a a day can do a piece of work in 18 days, in how many days will 21 men working 8 hrs. a day do the same piece of work?

Solution:

Step 1: We have to find the number of days hence write the given no. of days (i.e; 18) as numerator first.

Step 2: Number of men decreases, hence we will require more days. So out of the given values of men, we will write greater value as numerator and the smaller value as denominator.

                                                  i.e; 30/21 and not 21/30.

Step 3: Number of hours increases, hence we’ll require less days. So out of the given values of hours, we will write smaller value as numerator and the greater value as denominator.

                                                  i.e; 7/8 and not 8/7.

Now, multiply all the values obtained in sep 1, step 2 and step 3.

you need not to write all the steps, these steps have to be performed mentally, Believe us, if you understand the concept well, you will start solving the problems in seconds, most of the time mentally without using pen and paper.

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WORK AND TIME SHORTCUTS – RULE OF FRACTION