A 75-liter mixture contains milk and water in the ratio 3:2. If 15 liters of this mixture are removed and replaced with 10 liters of pure milk, what is the new ratio of milk to water in the mixture?

Correct — B. Split the 75 L by 3 : 2: milk 45 L, water 30 L.

The 15 L removed leaves in the same 3 : 2 ratio:
milk 15 × 3⁄5 = 9 L, water 15 × 2⁄5 = 6 L
Left: milk 45 − 9 = 36 L, water 30 − 6 = 24 L

Add 10 L of pure milk: milk = 36 + 10 = 46 L
New ratio = 46 : 24 = 23 : 12 → option (b)

Why the others are wrong

• (a)
  11:7 — Water stays at 24 L after the milk goes in, and the vessel holds 70 L. At 11 : 7, water would be 70 × 7⁄18 ≈ 27.2 L.
• (c)
  17:11 — At 17 : 11 the 70 L would split into 42.5 L of milk and 27.5 L of water, but only 24 L of water remains after the removal.
• (d)
  19:12 — It keeps water at 12 parts = 24 L, which makes milk 19 × 2 = 38 L. The vessel actually holds 36 + 10 = 46 L of milk.

Taking out part of a well-mixed solution removes every component in the mixture's own ratio. The ratio of what stays is unchanged; only the quantities shrink.

Adding a pure component changes one quantity alone. Water is fixed at 24 L once the 15 L is out, so it is the fastest check: the final 70 L must hold exactly 24 L of water, or 12⁄35 of the total.

Key facts

• Removing x litres of a mixture in ratio a : b removes x × a⁄(a + b) of the first and x × b⁄(a + b) of the second.
• 75 L at 3 : 2 holds 45 L of milk and 30 L of water.
• After the swap the vessel holds 70 L: 46 L of milk and 24 L of water.

Common traps

• Taking all 15 L out of the milk: milk falls to 30 L and the ratio becomes 40 : 30 = 4 : 3.
• Assuming the vessel is back to 75 L: only 10 L goes back in, so the total is 70 L.

No directly related past PYQ was found.