How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?

A. 1.0 litres

B. 1.5 litres

C. 2.0 litres

D. 4.0 litres

E. 4.0 litres

Question

How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?

A. 1.0 litres

B. 1.5 litres

C. 2.0 litres

D. 4.0 litres

E. 4.0 litres

Rakesh Rakesh · Answer

Let’s focus on the amount of milk in the solution, which has an initial concentration of 2/5 = 0.4. Thus, we start with 12 * 0.4 = 4.8 liters of milk in the solution. Then we remove x liters of solution that has a concentration of 0.4 milk. We then replace those x removed liters with pure milk with a concentration of 1.0 (i.e. 100% milk). The result is 12 liters of solution with a 0.5 concentration of milk.We can put all this information into an equation:(12 * 0.4) - (0.4 * x) + (1.0 * x) = 12 * 0.54.8 - 0.4x + x = 60.6x = 1.2x = 2Answer.C

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