Question
Mixture X comprises juice and water in a 5:4 ratio, and
mixture Y consists of juice and water in a 7:9 ratio. When mixture X is combined with mixture Y, the total quantity of the resulting mixture becomes ___ ml, and the quantity of water in mixture Y is ____ ml more than in mixture X. The ratio of the quantities of juice in mixture X to Y is ___. Determine which values, given in the following options, can fill the blanks in the correct order to make the statement true. I.) 590, 60, 15:14 II.) 756, 99, 20:21 III.) 1080, 100, 10:9 IV.) 1608, 252, 9:7Solution
ATQ, For statement I: Let quantity of juice and water in mixture X is '5x' ml and 4x ml respectively. Quantity of juice and water in mixture Y is '7y' ml and 9y ml respectively. So, 9x + 16y = 590..........................(1) And, 9y – 4x = 60.........................(2) Solving equation (1) and (2), we get x = 30 and y = 20 So, desired ratio = 150:140 = 15:14 So, statement I is true For statement II: Let quantity of juice and water in mixture X is '5x' ml and 4x ml respectively. Quantity of juice and water in mixture Y is '7y' ml and 9y ml respectively. So, 9x + 16y = 756..........................(1) And, 9y – 4x = 99.........................(2) Solving equation (1) and (2), we get x = 36 and y = 27 So, desired ratio = 180:189 = 20:21 So, statement II is true For statement III: Let quantity of juice and water in mixture X is '5x' ml and 4x ml respectively. Quantity of juice and water in mixture Y is '7y' ml and 9y ml respectively. So, 9x + 16y = 1080..........................(1) And, 9y – 4x = 100.........................(2) Solving equation (1) and (2), we get x = 56 and y = 36 So, desired ratio = 280:252 = 10:9 So, statement III is true. For statement IV: Let quantity of juice and water in mixture X is '5x' ml and 4x ml respectively. Quantity of juice and water in mixture Y is '7y' ml and 9y ml respectively. So, 9x + 16y = 1608..........................(1) And, 9y – 4x = 252.........................(2) Solving equation (1) and (2), we get x = 72 and y = 60 So, desired ratio = 360:420 = 6:7 So, statement IV is not true
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