Vessel A has 20 litres of a mixture of milk and water having...

Vessel $A$ has 20 litres of a mixture of milk and water having $75 \%$ milk. Vessel $B$ has $x$ litres of a mixture of milk and water having $60 \%$ milk. The contents of the vessels are mixed to form a mixture having $66 \%$ milk. Find $x$.
(A) 25
(B) 30
(C) 20
(D) 40

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Key Concepts

Percentage Composition

This concept refers to the proportion of a particular substance within a mixture, typically expressed as a percentage. It is used to determine the amount of each component (like milk or water) present in a mixture relative to the total volume.

Mixture Problems

Mixture problems involve combining two or more substances with different properties, such as concentration or percentage composition, to achieve a mixture with a desired characteristic. These types of problems require the application of proportional reasoning and balance of the overall mixture.

Weighted Average

The weighted average is a method for finding the average value when different items contribute unequally to the final result. In the context of mixture problems, it is used to combine the percentages of various components based on their relative volumes.

Algebraic Equation Solving

This concept involves setting up and solving equations based on the relationships defined in a problem. In mixture problems, algebra is used to establish equations that represent the balance of component amounts or percentages in the final mixture, and solving these equations yields unknown quantities.

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