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# Compound Proportion

## Introduction

Compound proportion is the proportion that involved between two or more quantities. It is the equality between many ratios. When there are more than two quantities Q1, Q2, Q3 their equalities can be obtained by using compound proportions. Their equalities can be obtained using different cases.

If Q1 contains variables a,b

Q2 contains variables c,d

Q3 Contains variables e,f then:

Case 1:

When they are directly related to each other i.e., Q1 and Q2 are directly related and Q2 and Q3 are also directly related then,

Compound relation:

$$\frac{aXb}{e} = \frac{cXd}{f}$$

Case 2:

When Q1 and Q2 are directly related and Q2 and Q3 are inversely related then,

Compound relation:

$$\frac{aXb}{e} = \frac{cXd}{f}$$

Case 3:

When Q1 and Q2 are inversely related and Q2 and Q3 are directly related then,

Compound relation:

$$\frac{aXb}{e} = \frac{cXd}{f}$$

Case 4:

When Q1 and Q2 are inversely related and Q2 and Q3 are also inversely related then,

Compound relation:

a x c x e = b x d x f

## Properties

1)Compound proportionality can only obtain when they are two are more quantities.

2)If they are only 2 quantities then we can only have normal proportionality.

## Solved Problems

1) A dairy form can fill 2000 liters of milk in 2 days using 2 machines.How many liters can be filled using 16 machine in 4 days?

Solution:

Machine Days liters

12 2 2000

16 4 x

Compound rate :$\frac{12 X 2}{2000}$ =$\frac{16 X 4}{x}$

24X=32000

X=1333.3liters

2) A shoe factory can manufacture 200 pairs of shoes in a day using 10 machines.How many pairs can be manufactured using 4 machines in 4 days?

Solution:

Machine Days pairs of shoes

10 1 200

14 4 x

Compound rate: $\frac{10 X 1}{200}$ =$\frac{14 X 4}{x}$

10 x 1 x (x) = 14 x 4 x 200

10x = 1120

x = 1120pairs.