Mixture of milk and water has been kept in two separate containers. ratio of…
2025
Mixture of milk and water has been kept in two separate containers. ratio of milk to water in one of the containers is 5:1 and that in the other container is 7:2. in what ratio the mixtures of these two containers should be added together so that the quantity of the milk in the new mixture may become 80%?
- A.
2:3
- B.
1:2
- C.
14:19
- D.
3:7
Attempted by 6 students.
Show answer & explanation
Correct answer: A
Given:
First mixture milk fraction = 5/(5+1) = 5/6. Second mixture milk fraction = 7/(7+2) = 7/9. Target milk fraction = 80% = 4/5.
Method 1 (algebraic): Let x and y be parts of the first and second mixtures. Solve (5/6)x + (7/9)y = (4/5)(x + y). Multiply both sides by 90 to clear denominators: 75x + 70y = 72x + 72y, so 3x = 2y and x:y = 2:3.
Method 2 (allegation): Compute differences from target: first - target = 5/6 - 4/5 = 1/30, target - second = 4/5 - 7/9 = 1/45. Ratio of parts = (1/45):(1/30) = 2:3.
Therefore, mix the two containers in the ratio 2:3 (first : second).