In what proportion must water be mixed with milk so as to gain 20% by selling mixture at cost price of milk?(water freely available)
The answer is 1:5 and the book says to gain 20% at cost price the milk should be 83.33% of new mixture so the ratio becomes 1:5. Can anyone please explain me how it is 83.33% and not 80%?
The profit margin on a trade is
$$ \frac{\textrm{Sale price}}{\textrm{Cost price}} - 1 $$
and you want this to equal 20%. Say the cost of milk is C, and you are going to mix a proportion F of milk, and (1 - F) of water. Then your sale price will be C (since you are selling it as milk) and your cost price is FC (since the water is free). Therefore you want
$$ \frac{C}{FC} - 1 = 0.2 $$
which rearranges to give
$$ F = \frac{1}{1.2} = 0.8333\dots $$