Multiple choice

Vessels A and B contain milk and water mixed in the ratio 5 : 2 and 7 : 6, respectively. In what ratio must these mixtures be mixed to form a new mixture in vessel C containing milk and water in the ratio 8 : 5?

  1. 6 : 9

  2. 7 : 9

  3. 8 : 9

  4. 9 : 10

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the method of alligation, the fraction of milk in vessel A is 5/7, in vessel B is 7/13, and in the mixture is 8/13. The difference between A and the mixture is |5/7 - 8/13| = |65-56|/91 = 9/91, and between B and the mixture is |7/13 - 8/13| = 1/13 = 7/91. The ratio is 7/91 : 9/91 = 7 : 9.

AI explanation

Using the method of Alligation on the milk concentrations, vessel A has a concentration of 5/7 and vessel B has a concentration of 7/13, while the target mixture C has a concentration of 8/13. The required ratio is (8/13 minus 7/13) to (5/7 minus 8/13), which simplifies to 1/13 to 9/91. By converting the first term to have a common denominator of 91, we get 7/91 to 9/91, meaning the mixtures must be combined in a ratio of 7 to 9.

Keep practicing — related questions