Multiple choice

Two vessels $A$ and $B$ contain milk and water in the ratio of $5 : 2$ and $2 : 3$. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio :

  1. $2 : 5$
  2. $7 : 3$
  3. $1 : 2$
  4. $4 : 5$
  5. $7 : 15$

  6. None of these 
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E Correct answer
Explanation

Use the rule of alligation. Vessel A: milk fraction 5/7. Vessel B: milk fraction 2/5. Target mixture: 1/2. Differences: |5/7 - 1/2| = 3/14 and |2/5 - 1/2| = 1/10. The ratio is (1/10) : (3/14) = 14 : 30 = 7 : 15.

AI explanation

By the rule of alligation on the milk concentrations, vessel A has a concentration of 5 sevenths and vessel B has a concentration of 2 fifths. The ratio of their required quantities is the difference between the target concentration of 1 half and vessel B concentration, placed over the difference between vessel A concentration and the target concentration. This establishes the ratio as 1 tenth divided by 3 thirty-fifths, which equals 7 to 15.

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