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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?
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There are 3 different jugs containing a mixture of wine and water in t...
Solution: 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.
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.
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, option 4.
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, option 4.
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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 : 3b)9 : 4c)8 : 1d)More than one of the aboveCorrect answer is option 'D'. Can you explain this answer?
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