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The methods to solve the problems for compound variation are:

- Proportion method
- Multiplicative factor method
- Formula method

**1**. Proportion method:

In this method, from the given data, determine whether they are in direct or inverse proportion. Then, the value of the unknown(\(x\)) can be determined using:

The product of the extremes \(=\) The product of the means

**2**. Multiplicative factor method:

Let us consider the table to understand how to solve the problem using the multiplicative factor method.

Quantity \(1\) | Quantity \(2\) | Quantity \(3\) |

\(a\) | \(b\) | \(c\) |

\(x\) | \(d\) | \(e\) |

Here, the unknown quantity is \(x\).

**Step 1**: Compare the unknown value (Quantity \(1\)) with the known values (Quantity \(2\) and Quantity \(3\)).

**Step 2**: If Quantity \(1\) and Quantity \(2\) are in direct variation, then take the multiplying factor as \(\frac{d}{b}\)(take the reciprocal).

**Step 3**: If Quantity \(1\) and Quantity \(3\) are in inverse variation, then take the multiplying factor as \(\frac{c}{e}\)(no change).

**Step 4**: The value of the unknown \(x\) can be determined using \(x = a \times \frac{d}{b} \times \frac{c}{e}\).

**3**. Formula method:

From the given data, identify Persons(\(P\)), Days(\(D\)), Hours(\(H\)) and Work(\(W\)) and use the formula:

\(\frac{P_1 \times D_1 \times H_1}{W_1} = \frac{P_2 \times D_2 \times H_2}{W_2}\)

Here, the suffix \(1\) denotes the values from statement \(1\), whereas the suffix \(2\) denotes the values from statement \(2\).