A 60-litre mixture has alcohol and water in the ratio 2 : 1. How much water must be added to make the ratio 1 : 2?
60 litres. The mixture has 40 L alcohol and 20 L water. Alcohol stays 40 L, and for 1 : 2 water must be 80 L. So add 80 - 20 = 60 litres of water.
Explain it simply
When you only add water, the alcohol does not change. So anchor everything on the alcohol. Work out how much water the new ratio requires for that same amount of alcohol, then subtract the water already there. Anchor on whichever component stays fixed.
Example
Question: 60 L of alcohol : water = 2 : 1. Add water to make 1 : 2.
- Alcohol = 60 x 2/3 = 40 L. Water = 20 L.
- New ratio 1 : 2 means water = 2 x alcohol = 80 L.
- Water to add = 80 - 20 = 60 L.
- New mixture = 120 L, with 40 L alcohol (1/3) and 80 L water (2/3).
Variation: if you remove x litres of the mixture and replace it with water to reach 1 : 1, alcohol after removal is 40 - (2/3)x and must equal 30 (half of 60). So x = 15 litres.
const alcohol = 40, water = 20;
console.log(2 * alcohol - water); // Output: 60
console.log(((40 - 30) * 3) / 2); // Output: 15What to say in the interview
"Adding water leaves the alcohol at 40 litres. For 1 to 2 I need 80 litres of water, and 20 are already there, so I add 60."
Common mistakes
- Adding water until the total is 60 or keeping the total fixed.
- Anchoring on water, which is the quantity that changes.