ruchi857 wrote:

Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4

A) 2:7

B) 5:2

C) 3:5

D) 5:7

We can create the ratios:

Vessel A:

milk : water = 8x : 5x and so 8x + 5x = 13x (Eq. 1)

Vessel B:

milk : water = 5y : 2y and so 5y + 2y = 7y (Eq. 2)

We can create the equation:

(8x + 5y)/(5x + 2y) = 9/4

4(8x + 5y) = 9(5x + 2y)

32x + 20y = 45x + 18y

2y = 13x (Eq. 3)

Notice that Eq. 1 stated that 8x + 5x = 13x; thus, in terms of y, we use Eq. 3 to state that vessel A has an amount of 2y, and vessel B has an amount of 5y + 2y = 7y (from Eq. 2). Thus, the ratio of the amount in vessel A to the amount in vessel B is 2y/7y = 2/7.

Answer: A

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