In a 30 L mixture, milk: water = 3:2. How much water must be added to make the ratio 1:1?

Correct — A.
Rule: only water is added, so the milk stays fixed.

Milk: 3⁄5 × 30 = 18 L
Water: 2⁄5 × 30 = 12 L

For 1 : 1, water must equal milk: 18 L
Water to add: 18 − 12 = 6 L → option (a).

Why the others are wrong

• (b)
  10 L — 10 L takes the water to 22 L against 18 L of milk, a ratio of 9 : 11. There is now more water than milk.
• (c)
  9 L — 9 L makes the water 21 L against 18 L of milk, which is 6 : 7, not 1 : 1.
• (d)
  12 L — 12 L doubles the water already present to 24 L. Milk to water is then 18 : 24 = 3 : 4.

When one part is added to a mixture, the other part is the anchor: its amount is the same before and after. Split the mixture by its ratio, hold the unchanged part fixed, and read the new amount of the added part from the target ratio.

Here 3 : 2 on 30 L gives 18 L of milk and 12 L of water. A 1 : 1 ratio needs the water to match the 18 L of milk.

Key facts

• A total T in the ratio a : b splits as a⁄(a + b) × T and b⁄(a + b) × T.
• 30 L at 3 : 2 is 18 L of milk and 12 L of water.
• Adding water changes the ratio but not the amount of milk.

Common traps

• Applying 1 : 1 to the old 30 L, 15 L each, and adding 3 L. The total grows as water goes in, so the water must reach 18 L.
• Adding as much water as is already there, 12 L, which gives 18 : 24 = 3 : 4

No directly related past PYQ was found.