ICSE Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------

**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:

- More articles, more cost
- More men, more will be the work done
- 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:

- More men would take less time to complete the job.
- 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 x 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).

ICSE Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------