Two containers of milk contain mixtures of water and milk in ratio 5:4 and…
2023
Two containers of milk contain mixtures of water and milk in ratio 5:4 and 7:9. In what ratio should they be mixed so that the final mixture is in ratio 6:6?
- A.
6:5
- B.
7:5
- C.
8:9
- D.
9:8
Attempted by 18 students.
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Correct answer: D
Solution:
Milk fraction in the first mixture (water:milk = 5:4) = 4/(5+4) = 4/9.
Milk fraction in the second mixture (water:milk = 7:9) = 9/(7+9) = 9/16.
Target final mixture 6:6 = 1:1, so desired milk fraction = 1/2.
Let x be parts of the first mixture and y be parts of the second. Set up the weighted average:
(4/9)x + (9/16)y = (1/2)(x + y).
Clear denominators by multiplying both sides by 144 (LCM of 9 and 16): 64x + 81y = 72x + 72y.
Rearrange: 64x + 81y = 72x + 72y ⇒ 8x = 9y ⇒ x:y = 9:8.
Therefore, mix the first and second mixtures in the ratio 9:8 to obtain the final 6:6 (1:1) mixture.