A 30 L mixture contains milk and water in the ratio 3:2. How much milk must be added to make it 4:1?
- (a)51 L
- (b)60 L
- (c)30 L
- (d)40 L
Answer
Why
Correct — C.
Rule: the liquid you do not add stays fixed, here the water.
Milk = 3⁄5 × 30 = 18 L
Water = 30 − 18 = 12 L
Milk for 4:1 = 4 × 12 = 48 L
Milk to add = 48 − 18 = 30 L → option (c)
Why the others are wrong
- (a)51 L — 51 L of milk would make 18 + 51 = 69 L against 12 L of water, a ratio of 23:4, not 4:1.
- (b)60 L — 60 L is the size of the new mixture (48 L milk + 12 L water), not the milk added. Adding 60 L gives 78:12 = 13:2.
- (d)40 L — 40 L of milk would make 58 L against 12 L of water, 29:6, about 4.8:1, more milk than 4:1 allows.
Concept
When one liquid is added to a mixture, the other liquid does not change. Anchor the new ratio on it.
Water stays at 12 L. In 4:1, milk = 4 × water, so milk must reach 48 L; it already has 18 L.
Check: 48 : 12 = 4 : 1, and the new mixture holds 60 L.
Key facts
- Adding one component leaves the other unchanged: water stays at 12 L.
- Milk in the original 30 L = 3⁄5 × 30 = 18 L.
- The final mixture is 48 L milk + 12 L water = 60 L.
Study next
Common traps
- Choosing 60 L, the final volume, instead of the 30 L actually added.
- Resetting the 30 L itself to 4:1 (24 L milk, 6 L water), which would mean removing water, not adding milk.
The same 30 L mixture at 3:2 appears at 18 Sep 2025, 12:30, Reasoning Q.19, where water is added to reach 1:1. Milk stays at 18 L there, so 6 L of water is keyed.
Related PYQs
No directly related past PYQ was found.