A mixture contains milk and water in the ratio 5:1. On adding 5 litres of water, the ratio of milk to water becomes 5 : 2. Find the quantity of milk in the mixture?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25 litres
Adding water changes only the water; the quantity of milk stays the same. Writing both quantities in terms of one unknown and using the new ratio gives that unknown.
Assuming milk \(=5x\) litres and water \(=x\) litres
After 5 litres of water are added: \(\displaystyle\frac{5x}{x+5}=\frac{5}{2}\)
\(10x=5x+25\), so the mixture had \(x=5\) litres of water to begin with
Milk \(=5x=25\) litres, the same before and after the water is added
Shortcut:
Milk is 5 parts in both ratios, so the parts are of the same size; water goes from 1 part to 2 parts
The extra 1 part is the 5 litres added, so milk \(=5\times5=25\) litres