An apprentice baker made 40 liters of 60% sugar syrup instead of 40 liters of 45% sugar syrup.

How much syrup should she drain and replace with distilled water so that the resulting solution is 40 liters of 45% syrup?

Solution:

Firstly, lets find the only syrup. 40 liters of 60% sugar syrup == 26 liters syrup and 16 litres water.

For the 45% syrup, we must add some woter. We have 26 liters syrup.

If we have a 45% sugar syrup, we need 31.7 liters water for 26 liters syrup.

At the begining, we had 16 liters water. So 31.7 – 16 = 15.6 liters added water.

How does one obtain 26 liters of syrup from 40 gallons of 60% concentration?