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A vessel contains liquids A and B in ratio 5 : 3. If 16 litres of the mixture are removed and the same quantity of liquid B is added the ratio becomes 3 : 5 What quantity does the vessel hold?
  • a)
    40 litres
  • b)
    50 litres
  • c)
    60 litres
  • d)
    one of the above
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A vessel contains liquids A and B in ratio 5 : 3. If 16 litres of the ...
 Suppose the vessel contains 5x litres and 3x litres of liquids A and B respectively.
The removed quantity contains = 16/(5 + 3) × 5 = 10litres of A and 16 - 10 = 6 litres of B
Now, (5x - 10) : (3x - 6 + 16) = 3 : 5
⇒ (5x - 10) / (3x + 10) = 3/5
⇒ 25x - 50 = 9x + 30
⇒ 16x = 80
⇒ x = 5
∴ Capacity of vessel = 8x = 8 × 5 = 40
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Most Upvoted Answer
A vessel contains liquids A and B in ratio 5 : 3. If 16 litres of the ...
Given:
- The ratio of liquids A and B in the vessel is 5:3.
- 16 liters of the mixture are removed.
- The same quantity of liquid B is added.
- The new ratio becomes 3:5.

To find:
- The quantity the vessel holds.

Solution:

Let's assume the initial quantity of liquid A in the vessel is 5x liters, and the initial quantity of liquid B is 3x liters.

Step 1: Calculate the initial quantity of the mixture:
The initial quantity of the mixture in the vessel = quantity of liquid A + quantity of liquid B
= 5x + 3x
= 8x liters

Step 2: Calculate the quantity of the mixture after 16 liters are removed:
The quantity of the mixture after 16 liters are removed = initial quantity of the mixture - 16
= 8x - 16 liters

Step 3: Calculate the quantity of liquid B after 16 liters are removed:
The quantity of liquid B after 16 liters are removed = initial quantity of liquid B - 16
= 3x - 16 liters

Step 4: Calculate the quantity of liquid B added:
The quantity of liquid B added = quantity of liquid B after 16 liters are removed
= 3x - 16 liters

Step 5: Calculate the quantity of the mixture after the same quantity of liquid B is added:
The quantity of the mixture after the same quantity of liquid B is added = quantity of the mixture after 16 liters are removed + quantity of liquid B added
= (8x - 16) + (3x - 16)
= 11x - 32 liters

Step 6: Calculate the new ratio:
The new ratio of liquids A and B = quantity of liquid A : quantity of liquid B
= 5x : (3x - 16)

According to the given information, the new ratio is 3:5. So, we can set up the following equation:

5x / (3x - 16) = 3 / 5

Cross multiplying, we get:

5 * 3x = (3x - 16) * 5
15x = 15x - 80
15x - 15x = -80
0 = -80

This equation is not possible to solve, as it leads to an inconsistency. Therefore, the given information is not consistent, and we cannot determine the quantity the vessel holds.

So, the correct answer is d) one of the above.
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A vessel contains liquids A and B in ratio 5 : 3. If 16 litres of the mixture are removed and the same quantity of liquid B is added the ratio becomes 3 : 5 What quantity does the vessel hold?a)40 litresb)50 litresc)60 litresd)one of the aboveCorrect answer is option 'A'. Can you explain this answer?
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A vessel contains liquids A and B in ratio 5 : 3. If 16 litres of the mixture are removed and the same quantity of liquid B is added the ratio becomes 3 : 5 What quantity does the vessel hold?a)40 litresb)50 litresc)60 litresd)one of the aboveCorrect answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A vessel contains liquids A and B in ratio 5 : 3. If 16 litres of the mixture are removed and the same quantity of liquid B is added the ratio becomes 3 : 5 What quantity does the vessel hold?a)40 litresb)50 litresc)60 litresd)one of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel contains liquids A and B in ratio 5 : 3. If 16 litres of the mixture are removed and the same quantity of liquid B is added the ratio becomes 3 : 5 What quantity does the vessel hold?a)40 litresb)50 litresc)60 litresd)one of the aboveCorrect answer is option 'A'. Can you explain this answer?.
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