Two vessels contain milk and water in the ratios 3 : 1 and 5 : 3. If equal quantities from both are mixed, what is the ratio of milk to water?
11 : 5. Milk fractions are 3/4 and 5/8. Taking one litre from each gives milk 3/4 + 5/8 = 11/8 litres out of 2, so milk is 11/16 and water 5/16 of the mixture.
Explain it simply
You cannot add ratios like 3 : 1 and 5 : 3 directly, because each is out of a different total (4 parts and 8 parts). Convert each to the fraction of milk in one litre, then add actual quantities. Taking a convenient equal amount, like 8 litres from each, keeps the numbers whole.
Example
Question: Vessel A milk : water = 3 : 1, vessel B = 5 : 3. Mix equal volumes.
Take 8 litres from each (8 is the LCM of 4 and 8).
| Milk | Water | |
|---|---|---|
| A (8 L) | 6 | 2 |
| B (8 L) | 5 | 3 |
| Total (16 L) | 11 | 5 |
Milk : water = 11 : 5.
If the volumes were not equal, say 2 litres of A for every 3 litres of B, scale the rows: A (8 L) gives 6 : 2 and B (12 L) gives 7.5 : 4.5, total 13.5 : 6.5 = 27 : 13.
const milk = 8 * (3 / 4) + 8 * (5 / 8);
const water = 16 - milk;
console.log([milk, water]); // Output: [11,5]What to say in the interview
"I pick a common quantity, 8 litres, so each vessel's milk and water are whole numbers: 6 and 2, then 5 and 3. Adding gives 11 to 5."
Common mistakes
- Adding ratios term by term to get 8 : 4 = 2 : 1.
- Ignoring the actual volumes taken when they are unequal.