Theory:

In direct proportion, two quantities \(x\) and \(y\) are said to increase (or decrease) together in such way that the ratio of their respective values is constant.
 
bb.PNG
 
That is to suggest, if \(\frac{x}{y} =\) \(k\) is positive, then \(x\) and \(y\) will differ directly. That is, \(x\) and \(y\) are in direct proportion.
When the quantities \(x\) and \(y\) are in direct proportion, we can write x1x2 \(=\) y1y2. Where y1, y2 are values of \(y\) corresponding to the values x1, x2 of \(x\).
Example:
 If \(1\) part of a sugar requires \(75 mL\) of water, how much part of sugar should we mix with \(1800 mL\) of water?
 
1z.PNG
 
Let the parts of sugar mix with \(1800 mL\) water be \(x\).              
 
Practically, if \(1\) part of a sugar requires \(75 mL\), of water, then \(1800 mL\) of water requires more sugar. 
 
Increase in quantity of water increases the quantity of sugar. So it is in direct proportion.
When the quantities \(x\) and \(y\) are in direct proportion, we can write x1x2 \(=\) y1y2. Where y1, y2 are values of \(y\) corresponding to the values x1, x2 of \(x\).
Substitute the known values in the formula.
 
\(\frac{1}{75}\) \(=\) \(\frac{x}{1800}\)
 
\(75\) × \(x\) \(=\) \(1\) × \(1800\)
 
\(x =\) \(\frac{1800}{75}\)
 
\(x =\) \(24\)
 
Hence, \(24\) parts sugar should be mixed with the water of \(1800 mL\).