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A container has a mixture of two liquids in the ratio 7:3. If 20 liters of the m

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Question: A container has a mixture of two liquids in the ratio 7:3. If 20 liters of the mixture is removed, what is the new ratio if the remaining mixture is 50 liters?

Options:

  1. 7:3
  2. 6:4
  3. 5:5
  4. 8:2

Correct Answer: 7:3

Solution: 

Initial volume = 50 + 20 = 70 liters. A = (7/10) * 70 = 49 liters, B = 21 liters. New ratio = 49:21 = 7:3.

A container has a mixture of two liquids in the ratio 7:3. If 20 liters of the m

Practice Questions

Q1
A container has a mixture of two liquids in the ratio 7:3. If 20 liters of the mixture is removed, what is the new ratio if the remaining mixture is 50 liters?
  1. 7:3
  2. 6:4
  3. 5:5
  4. 8:2

Questions & Step-by-Step Solutions

A container has a mixture of two liquids in the ratio 7:3. If 20 liters of the mixture is removed, what is the new ratio if the remaining mixture is 50 liters?
  • Step 1: Understand that the initial ratio of the two liquids is 7:3.
  • Step 2: Add the parts of the ratio together: 7 + 3 = 10 parts total.
  • Step 3: Calculate the total initial volume of the mixture before removing any liquid. Since 20 liters were removed and 50 liters remain, the initial volume is 50 + 20 = 70 liters.
  • Step 4: Find the volume of liquid A (the first liquid) in the initial mixture. Since A is 7 parts out of 10, calculate (7/10) * 70 = 49 liters.
  • Step 5: Find the volume of liquid B (the second liquid) in the initial mixture. Since B is 3 parts out of 10, calculate (3/10) * 70 = 21 liters.
  • Step 6: After removing 20 liters, the volumes of A and B remain the same because the mixture is uniform. So, A = 49 liters and B = 21 liters.
  • Step 7: Calculate the new ratio of A to B. The new ratio is 49:21.
  • Step 8: Simplify the ratio 49:21. Both numbers can be divided by 7, resulting in 7:3.
  • Ratio and Proportion – Understanding how to calculate and manipulate ratios when dealing with mixtures.
  • Volume Calculation – Calculating the total volume of a mixture before and after a portion is removed.
  • Mixture Problems – Applying the concept of ratios to find the new composition of a mixture after a certain volume is taken out.
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