A dishonest grocer claims to sell pure milk at cost price, but he mixes it with water and thereby gains 25%. Find the percentage of water in the mixture, assuming that water costs nothing.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20%
He sells every litre of mixture at the cost price of milk, so his whole gain comes from the water. A gain of 25% on the milk means the water is 25% of the milk, but the question asks for its share of the mixture.
Take 100 litres of milk; the gain of 25% needs 25 litres of water sold as milk
Mixture \(=100+25=125\) litres
Water % \(\displaystyle =\frac{25}{125}\times100=20\%\)
The mixture contains 20% water.
Why the other options are incorrect
Option (1) 25% — Incorrect. 25 litres is water per 100 litres of milk, not per 100 litres of mixture.
Option (3) 18% — Incorrect. 18% water would give a gain of \(18\div82\), about 22%.
Option (4) 22% — Incorrect. 22% water would give a gain of \(22\div78\), about 28%.