A milk vendor has 2 cans of milk. The first contains 25% water and the rest…
2026
A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
- A.
4 litres, 8 litres
- B.
6 litres, 6 litres
- C.
5 litres, 7 litres
- D.
7 litres, 5 litres
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Correct answer: B
Improved solution:
Find the milk fractions in each container: the first contains 25% water so milk = 75% = 3/4; the second contains 50% water so milk = 1/2.
Desired final ratio water:milk = 3:5 so milk fraction = 5/(3+5) = 5/8. For a 12-litre mixture, milk needed = 12 × 5/8 = 7.5 litres.
Let x litres be taken from the first container and (12 − x) litres from the second. Total milk contributed = (3/4)x + (1/2)(12 − x). Set this equal to 7.5 and solve:
(3/4)x + (1/2)(12 − x) = 7.5
(3/4)x + 6 − (1/2)x = 7.5 ⇒ (1/4)x = 1.5 ⇒ x = 6
Thus take 6 litres from the first container and 6 litres from the second. Total milk = 0.75×6 + 0.5×6 = 7.5 litres, which matches 5/8 of 12 litres, so the required water:milk ratio 3:5 is achieved.