A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

Question

A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was

Answer 1

Here's the rephrased HTML with clearer and more concise explanatory text:

Let the original solution contain \( x \) liters of water and \( y \) liters of acid.

When 2 liters of water are added, the new volume of water is \( x + 2 \) liters, with the acid volume remaining \( y \) liters.

This new solution is 50% acid, which can be expressed as:

\[ \frac{y}{x + 2} = 0.5 \]

Next, 15 liters of acid are added. The solution now has:

Water: \( x + 2 \), Acid: \( y + 15 \)

This final solution is 80% acid, leading to the equation:

\[ \frac{y + 15}{x + 2 + 15} = 0.8 \]

Solving these two equations yields:

\[ x = 2, \quad y = 7 \]

Thus, the original solution's water to acid ratio is \( 2 : 7 \), or equivalently \( 1 : 3.5 \).

The Correct Option is A

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