Aulia22 wrote:
A and B containing spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8:5 ?
a) 4:3
b) 3:4
c) 5:6
d) 7:9
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We can let 5x and 2x be the amount of spirit and water in mixture A and let 7y and 6y be the amount of spirit and water in mixture B. The new mixture will contain (5x + 7y) spirit and (2x + 6y) water, and the spirit : water ratio will be 8:5. Thus, we can create the equation:
(5x + 7y)/(2x + 6y) = 8/5
5(5x + 7y) = 8(2x + 6y)
25x + 35y = 16x + 48y
9x = 13y
x/y = 13/9
Therefore, the ratio of the two mixtures A and B is (7x)/(13y) = (7/13) * (x/y) = (7/13) * (13/9) = 7/9.
Answer: D
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