Question
Two mixtures, 'A' and 'B', each consist of milk and
water. Mixture 'A' is composed of __% water, with the remaining percentage being milk. Mixture 'B' contains the same volume of water as mixture 'A' but differs in its milk content. Both mixtures are transferred into a container with a total capacity of 600 liters. To ensure the container is filled to its maximum capacity, an additional 50 liters of water is added. Given that the final milk-to-water ratio in the container is 7:5, determine the volume of milk in mixture 'B', which is a ___ liter. The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true: I. 25, 50 II. 40, 200 III. 50, 250Solution
Quantity of water in the container = 600 X (5/12) = 250 litres So, quantity of water in the two mixtures together = 250 - 50 = 200 litres So, quantity of water in each mixture = 200 ÷ 2 = 100 litres For I: Let the total quantity of mixture 'A' be 'x' litres. ATQ; 0.25x = 100 So, x = 400 So, quantity of mixture 'B' = 600 - 50 - 400 = 150 litres So, quantity of milk in mixture 'B' = 150 - 100 = 50 litres So, statement I is true. For II: Let the total quantity of mixture 'A' be 'x' litres. ATQ; 0.4x = 100 So, x = 250 So, quantity of mixture 'B' = 600 - 50 - 250 = 300 litres So, quantity of milk in mixture 'B' = 300 - 100 = 200 litres So, statement II is true. For III: Let the total quantity of mixture 'A' be 'x' litres. ATQ; 0.5x = 100 So, x = 200 So, quantity of mixture 'B' = 600 - 50 - 200 = 350 litres So, quantity of milk in mixture 'B' = 350 - 100 = 250 litres So, statement III is true. Hence, option d.
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