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 A vessel which contains a mixture of acid and water in ratio 13:4. 25.5 litres of mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of acid is added to the mixture. If resultant mixture contains 25% water, what was the initial quantity of mixture in the vessel before the replacement in litres?
  • a)
    58 litre
  • b)
    68 litre
  • c)
    78 litre
  • d)
    48 litre
  • e)
    None of the Above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A vessel which contains a mixture of acid and water in ratio 13:4. 25....
Answer – B. 68 litre Explanation : Quantity of Acid = 13x Quantity of water = 4x Total = 17x Resultant Mixture = 17x – 25.5 + 2.5 + 5 = 17x – 18 Resultant water = 4x – 25.5 * (4/17) + 2.5 = 4x – 3.5 Resultant mixture contains 25% water (17x – 18)*25/100 = 4x – 3.5 x = 4 Initial quantity = 17*4 = 68
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A vessel which contains a mixture of acid and water in ratio 13:4. 25....
Problem: A vessel contains a mixture of acid and water in ratio 13:4. 25.5 litres of mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of acid is added to the mixture. If resultant mixture contains 25% water, what was the initial quantity of mixture in the vessel before the replacement in litres?

Solution:

Let the initial quantity of the mixture be x litres.

Given that the ratio of acid and water in the mixture is 13:4.

Let the quantity of acid in the mixture be 13y and the quantity of water be 4y.

Therefore, the total quantity of the mixture = 13y + 4y = 17y

It is also given that 25.5 litres of mixture is taken out from the vessel.

Therefore, the remaining quantity of the mixture = x - 25.5 litres

Now, 2.5 litres of pure water is added to the mixture.

Therefore, the quantity of water in the mixture becomes 4y + 2.5 litres.

Also, 5 litres of acid is added to the mixture.

Therefore, the quantity of acid in the mixture becomes 13y + 5 litres.

It is given that the resultant mixture contains 25% water.

Therefore, we can write the equation as follows:

(4y + 2.5)/(13y + 5) = 1/4

Solving this equation, we get y = 1.25

Substituting the value of y in the equation 17y, we get the initial quantity of mixture in the vessel as 68 litres.

Therefore, the correct answer is option (b) 68 litres.
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A vessel which contains a mixture of acid and water in ratio 13:4. 25.5 litres of mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of acid is added to the mixture. If resultant mixture contains 25% water, what was the initial quantity of mixture in the vessel before the replacement in litres?a)58 litreb)68 litrec)78 litred)48 litree)None of the AboveCorrect answer is option 'B'. Can you explain this answer?
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