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Jar A contains ‘X’ L of pure milk only. A 27 L mixture of milk and water in the respective ratio of 4 : 5, is added into it. If the new mixture thus formed in jar A contains 70% milk, what is the value of X?

A23L

B27L

C30L

D48L

Answer:

A. 23L

Read Explanation:

Understanding Mixture Problems in Competitive Exams

  • Mixture and Alligation is a very common topic in quantitative aptitude sections of competitive exams, testing a candidate's ability to work with ratios, percentages, and basic algebra.

  • The core idea is to combine different substances (like milk and water, or different solutions) and determine the properties of the resulting mixture.

Step-by-Step Solution Breakdown

  • Initial State: Jar A initially contains only pure milk. Let its volume be X Litres. Since it's pure milk, the water content is 0 Litres.

  • Analyzing the Added Mixture: A 27 Litre mixture of milk and water is added. The ratio of milk to water in this mixture is 4:5.

    • To find the quantity of milk in this 27 L mixture: Milk = (Ratio of Milk / Sum of Ratios) * Total Volume = (4 / (4 + 5)) * 27 = (4/9) * 27 = 12 Litres.

    • To find the quantity of water in this 27 L mixture: Water = (Ratio of Water / Sum of Ratios) * Total Volume = (5 / (4 + 5)) * 27 = (5/9) * 27 = 15 Litres.

  • Calculating the Components of the New Mixture in Jar A:

    • Total Milk: The original milk in Jar A (X Litres) + milk from the added mixture (12 Litres) = (X + 12) Litres.

    • Total Water: The original water in Jar A (0 Litres) + water from the added mixture (15 Litres) = 15 Litres.

    • Total Volume of New Mixture: Sum of total milk and total water = (X + 12) + 15 = (X + 27) Litres.

  • Formulating the Equation Based on Final Percentage: It is given that the new mixture contains 70% milk.

    • The percentage of milk is calculated as (Total Milk / Total Volume of Mixture) * 100%.

    • So, (X + 12) / (X + 27) = 70 / 100.

    • Cross-multiplying: 100 * (X + 12) = 70 * (X + 27).

    • Expanding the equation: 100X + 1200 = 70X + 1890.

    • Rearranging to solve for X: 100X - 70X = 1890 - 1200.

    • 30X = 690.

    • X = 690 / 30 = 23 Litres.


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