A vessel contains 180 liters of a mixture of milk and water in the ratio 5 :…
2025
A vessel contains 180 liters of a mixture of milk and water in the ratio 5 : 1. 40% of the mixture is taken out and x liters of pure milk is added to the mixture. If the ratio of milk to water in the resultant mixture becomes 7 : 1, then find the value of x.
- A.
32
- B.
60
- C.
48
- D.
36
- E.
48
Attempted by 3 students.
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Correct answer: D
Concept: When a fraction of a uniform mixture is removed, every component leaves in the SAME proportion, so the milk:water ratio of the leftover is unchanged. Removing 40% leaves 60% of EACH component. Adding pure milk increases only the milk; the water stays fixed. So pin down the water, then find the milk needed for the target ratio.
Split the original 180 L by the 5 : 1 ratio (6 equal parts): Milk = (5/6) x 180 = 150 L, Water = (1/6) x 180 = 30 L.
Remove 40% of the mixture, i.e. keep 60% of each component: Milk left = 0.6 x 150 = 90 L, Water left = 0.6 x 30 = 18 L.
Add x litres of pure milk. Water is unchanged at 18 L; milk becomes (90 + x). Set the new ratio: (90 + x) : 18 = 7 : 1.
Solve: 90 + x = 7 x 18 = 126, so x = 126 - 90 = 36 litres.
Cross-check: with x = 36, milk = 126 L and water = 18 L, and 126 : 18 = 7 : 1. Correct.