If a mixture contains milk and water in the ratio 4 : 1, and 20% of the…
2021
If a mixture contains milk and water in the ratio 4 : 1, and 20% of the mixture is taken out and then the same quantity is added back as equal amounts of milk and water, the difference between milk and water in the final mixture becomes 72 litres. Find the initial amount of the mixture.
- A.
120 liter
- B.
180 liter
- C.
90 liter
- D.
150 liter
- E.
None of these
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Concept
When a fraction of a uniform mixture is removed, the remaining liquid keeps the ORIGINAL ratio, so each component falls by that same fraction. Track milk and water as separate quantities through every step, then compute their difference. Here the difference depends only on the total, giving a single linear equation.
Application
Let the initial total mixture be T litres. With milk : water = 4 : 1, milk = (4/5)T and water = (1/5)T.
Remove 20% of the mixture. Since the removed part has the same 4 : 1 ratio, milk lost = (4/5)(0.2T) = 0.16T and water lost = (1/5)(0.2T) = 0.04T. Remaining milk = 0.64T, remaining water = 0.16T.
Add back the same quantity, 0.2T, as equal amounts of milk and water: 0.1T milk and 0.1T water. Final milk = 0.64T + 0.1T = 0.74T; final water = 0.16T + 0.1T = 0.26T.
Difference = final milk − final water = 0.74T − 0.26T = 0.48T.
Set 0.48T = 72, so T = 72 / 0.48 = 150 litres.
Cross-check
With T = 150: milk = 120, water = 30. After removal: milk = 96, water = 24. After adding 15 + 15: milk = 111, water = 39. Difference = 111 − 39 = 72 litres, matching the given value.