Class 8: Unitary Method (Lecture Notes)

Unitary Method: A method, in which the value of a unit quantity is first obtained to find the value of any other required quantity, is called unitary method. The basic rules applied in this method are:

To get more, we multiply
To get less, we divide

In solving problems based on unitary method, we come across two types of variations:

Direct Variation
Indirect Variation

Direct Variation: If two variables are so related to each other that an increase (or decrease) in the first causes an increase (or decrease) in the second, then the two variables are said to vary directly. They are directly proportion to each other.

Examples:

1. More articles, more cost
2. More men, more will be the work done
3. More working hours, more will be the work done

Rule for Solving Problems Based on Direct Variation: When, the value of a certain quantity of a variable is given then first ·we divide the given value by the given quantity to find the value of one unit. Now to find the value of a certain quantity, we multiply this quantity with the value of one unit.

Example: $10$ pens cost $150$ Rupees. Therefore one pen would cost ( $150/10 = 15$ Rupees). Therefore if you have to find the cost of $2$ pens, it would be $2$ multiplied by $15$ which would be $30$ Rupees.

Indirect Variation: If two variables are so related to each other that an increase (or decrease) in the first causes a decrease (or increase) in the other, then the two variables are said to vary indirectly or are inversely proportional.

Examples:

1. More men would take less time to complete the job.
2. High speed would reduce the time taken to reach the destination.

Rule for Solving Problems Based on Direct Variation: When the value of a certain quantity of a variable is given, then first we multiply the given value by the given quantity to find the value of one unit. Now, to find the value of certain quantity we divide the value of one unity by this quantity.

Example: Let us say that $10$ men finish the work in $10$ days. Therefore, one man can finish the work in $10 \times 10 = 100$ days. i.e. total work to be completed is $100$ man days. Hence, if we were to put $50$ men, then the work would get done in ( $100/50 = 2$ days).