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Chapter 10: Direct and Inverse Proportions

    Introduction

    Direct Proportion

    Inverse Proportion

    Compound Proportion

    Exercise 10.1

    Exercise 10.2

    Exercise 10.3

    Exercise 10.4

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worrksheet

    Hard Level Worksheet

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Chapter 10: Direct and Inverse Proportions > What We Have Discussed?

What We Have Discussed?

If x and y are in direct proportion, the two quantities vary in the same ratio i.e. if xy = k or x = . We can write x1y1 = x2y2 or x1 : y1 = x2: y2 (y1,y2 are values of y corresponding to the values x1, x2 of x respectively)

Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = between them, k being a constant. If y1 , y2 are the values of y corresponding to the values x1 and x2 of x respectively, then x1 y1 = x2 y2 (= k), or x1x2 = y2y1

If one quantity increases (decreases) as the other quantity decreases (increases) in same proportion, then we say it varies in the ratio of the other quantity.

The ratio of the first quantity (x₁:x₂) is equal to the ratio of the second quantity (y₂:y₁). As both the ratios are the same, we can express this inverse variation as proportion and it is called inverse proportion.

Sometimes change in one quantity depends upon the change in two or more other quantities in same proportion. Then we equate the ratio of the first quantity to the compound ratio of the other two quantities.