Question

A vessel of 160 L is filled with milk and water. 70% of milk and 30% of water is taken out of the vessel. It is found that the vessel is vacated by 55%. Find the quantity of milk and water in this mixture.

• A. Milk = 100 L; Water = 60 L
• B. Milk = 90 L; Water = 70 L
• C. Milk = 60 L; Water = 100 L
• D. None of these

Answer 1

Answer:

A. Milk = 100 L; Water = 60 L

Understanding Mixture Problems

• Mixture problems frequently appear in competitive exams, testing your ability to form and solve linear equations based on given percentages and total quantities.

• The core idea is to represent unknown quantities with variables and translate the given information into algebraic equations.

Setting Up the Equations

• Let 'M' be the initial quantity of milk in liters.

• Let 'W' be the initial quantity of water in liters.

• The total volume of the vessel is 160 L. Therefore, our first equation is:
  Equation 1: M + W = 160

Calculating the Quantities Removed

• It is stated that 70% of milk and 30% of water is taken out.

  • Quantity of milk taken out = 0.70 * M

  • Quantity of water taken out = 0.30 * W

• The vessel is vacated by 55% of its total volume.

  • Total volume vacated = 55% of 160 L = 0.55 * 160 = 88 L

• The total quantity taken out is the sum of milk taken out and water taken out, which must equal the total vacated volume. Therefore, our second equation is:
  Equation 2: 0.70M + 0.30W = 88

Solving the System of Equations

• We now have a system of two linear equations with two variables:

  • M + W = 160

  • 0.7M + 0.3W = 88

• A common method to solve this is substitution:

  • From Equation 1, express W in terms of M: W = 160 - M

  • Substitute this value of W into Equation 2:

  • 0.7M + 0.3(160 - M) = 88

  • 0.7M + 48 - 0.3M = 88

  • Combine like terms: 0.4M + 48 = 88

  • Subtract 48 from both sides: 0.4M = 88 - 48

  • 0.4M = 40

  • Divide by 0.4 to find M: M = 40 / 0.4 = 400 / 4 = 100 L

  • Now substitute the value of M back into W = 160 - M:

  • W = 160 - 100 = 60 L