Question

In a mixture of 150 L, the ratio of milk to water is 2 : 1. What amount of water must be further added to the mixture so as to make the ratio of the milk to water 1 : 2 respectively?

• A. 145L
• B. 160L
• C. 150L
• D. Other than those given as options

Answer 1

Answer:

C. 150L

Understanding Mixture Problems and Ratios

• Initial State Calculation:
  

  • The total volume of the mixture is 150 L.

  • The initial ratio of Milk to Water is 2 : 1. This means the mixture is divided into 2 + 1 = 3 parts.

  • Quantity of Milk = (2/3) * 150 L = 100 L.

  • Quantity of Water = (1/3) * 150 L = 50 L.

• Identifying the Constant Component:
  

  • When water is added to the mixture, the quantity of milk remains constant. This is a crucial concept in mixture problems.

  • The milk quantity will remain 100 L even after water is added.

• Target Ratio and New Water Calculation:
  

  • The desired new ratio of Milk to Water is 1 : 2.

  • Since the milk quantity is 100 L and it represents '1 part' in the new ratio (1:2), then '2 parts' (water) must be double the milk quantity.

  • New Quantity of Water = 2 * Quantity of Milk = 2 * 100 L = 200 L.

• Determining the Amount of Water Added:
  

  • The amount of water to be added is the difference between the new water quantity and the initial water quantity.

  • Water Added = New Water Quantity - Initial Water Quantity = 200 L - 50 L = 150 L.