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There are 3 different jugs containing a mixture of wine and water in the ratio 3 : 1, 1 : 1 and 10 : 1 respectively. If the mixtures are combined into a large jug, what may be the ratio of wine and water in the jug, if each jug has an integral amount of solution?
  • a)
    13 : 3
  • b)
    9 : 4
  • c)
    8 : 1
  • d)
    More than one of the above
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
There are 3 different jugs containing a mixture of wine and water in ...
Let the common ratio for the three jugs be respectively x, y and z.
Total amount of wine = 3x + y + 10z And, total amount of water = x + y + z.
Now, consider each option and see if it can be solved for an integral solution.
Option 1: (3x + y + 10z): (x + y + z) = 13 : 3 9x + 3y + 30z = 13x + 13y + 13z. so 4x + 10y = 17z This equation is satisfied for x = 1, y = 3 and z = 2
Hence, this ratio is possible.
Because of option 4, you still need to check options 2 and 3.
Start with option 3, as it is a simpler ratio.
Option 3: (3x + y + 10z): (x + y + z) = 8 : 1. 3x + y + 10z = 8x + 8y + 8z.
5x + 7y = 2z
This equation is satisfied for x = 1, y = 5 and z = 20. Hence, this ratio is also possible. Hence, the correct option is (d).
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