Theory:

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 \(2\).