If a 10 lit. mixture contains milk and water in the ratio 2:1 then, how much…
2023
If a 10 lit. mixture contains milk and water in the ratio 2:1 then, how much more water should be added to change the ratio to 1:2 ?
- A.
10
- B.
5
- C.
12
- D.
8
Attempted by 38 students.
Show answer & explanation
Correct answer: A
Clarification: The phrase "how much more mixture should be added" is ambiguous. Adding more of the same mixture will keep the milk:water ratio at 2:1, so the intended change to 1:2 requires adding only water. The steps below show that calculation.
Start:
Total mixture = 10 L; milk : water = 2 : 1.
Milk = (2/3)·10 = 20/3 L; water = (1/3)·10 = 10/3 L.
Let y be the litres of water to add. After adding, milk remains 20/3 L and water becomes 10/3 + y L. We want the new ratio milk:water = 1:2.
Set up the equation: (20/3) / (10/3 + y) = 1/2.
Solve: (20/3)·2 = 10/3 + y ⇒ 40/3 = 10/3 + y ⇒ y = 40/3 − 10/3 = 30/3 = 10.
Answer: Add 10 litres of water.