**Introduction about Study coefficient of proportionality:**

The relation between the two variables is known as proportionality and the ratio between these two variables is constant. The math sign ‘alpha’is used to represent proportionality. We have two types of proportionality can be:

(a) Direct Proportionality (we know that two variables are directly proportional.)

(b) Inverseproportionality (We know that two variables are indirectly proportional.)Here we are going to study about study coefficient of proportionality.

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## Example problems of study proportionality in study coefficient of proportionality:

**Example 1: **

A bus takes to travels 200 miles in 4 hours. How long the bus travels in 8 hours?

**Solution:**

**Step 1: **

Consider the problem as if takes 4 hour then the bus travel 200 miles. If a bus travel 8 hours how many miles the bus travel?

**Step 2:** it’s the direct proportionality.

**Step 3:** We know that

Hour’s miles

4 200

8 x

**Step 4:** Now we need to solve the value of x using cross multiplication. So, we get 4x="1600(Here" the coefficient of x is 4)

**Step 5:** Divide using 4 on both the sides. So, the bus travelled 400 miles.

This is the example of direct proportionality in study coefficient of proportionality.

Between, if you have problem on these topics Linear Regression Problem , please browse expert math related websites for more help on cbse guide for class 11.

## Inverse proportionality study coefficient of proportionality:

**Example2:**

Four pipes can fill a tank in 70 minutes. How long will it take to fill the tank by 7 pipes?

**Solution:**

**Step 1: **we know that four pipes can fill a tank in 70 minutes. We need to find how long will it take to fill the tank by 7 pipes?

**Step 2:** Number of pipes time taken

4 70

7 x

**Step 3:** Here the number of pipes is increased . So , this is the inverse proportionality.

**Step 4:** Now we need to find the value of x .

**Step 5:** therefore, x="` (4 times 70) /(7)` ..Now we have `280/7` .

**Step 6:** therefore, the answer is 40 minutes. (the tank needed 40 minutes )

Thisis the example of inverse proportionality in study coefficient of proportionality. These are the example problems of study coefficient proportionality.