Multiple choice

There are two mixtures i.e. P and Q of spirit and water. The mixture P contains ratio of spirit to water as 5 : 8 and Q contains ratio of water to spirit as 4 : 5. 26 litres of mixture P and some quantity of Q is taken out and these two quantities are mixed together to form a new mixture. Ratio of spirit to water in this new mixture is 4 : 5. Find the quantity which was taken out from Q.

  1. 14

  2. 8

  3. 12

  4. 10
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A Correct answer
Explanation

Mixture P: Spirit/Water = 5:8. In 26L, Spirit = 10L, Water = 16L. Mixture Q: Water/Spirit = 4:5, so Spirit/Water = 5:4. Let x be the quantity of Q. Spirit = 10 + (5/9)x, Water = 16 + (4/9)x. Ratio (10 + 5/9x) / (16 + 4/9x) = 4/5. Cross-multiplying: 50 + 25/9x = 64 + 16/9x. 9/9x = 14, so x = 14.

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