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Mixture P of lime juice and water contains 45% lime juice and the rest water. x ml of lime juice and 2x ml of water are added to mixture P such that the ratio of lime juice to water in the resultant mixture becomes 15:23. Find the ratio of the initial quantity of mixture P to x.

1. 5:7
2. 6:11
3. 3:7
4. 10:3

Correct answer: 10:3

Solution

Let the initial quantity of mixture be M. Then lime juice = 45% of M and water = 55% of M. After adding x ml lime juice and 2x ml water, the ratio becomes 15:23, which gives an equation in M and x. Solving it yields M:x = 10:3.

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