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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 $$2$$.