A mixture contains alcohol and water in the ratio 4 : 3. After 5 litres of water are added to the mixture, the ratio becomes 4 : 5. What is the quantity of alcohol in the original mixture?

Introduction / Context:
This problem is about mixture and ratio. We are told the initial ratio of alcohol to water in a mixture and how the ratio changes after adding a known amount of water. Questions of this type are standard in aptitude tests and require forming algebraic equations from ratios, then solving for the unknown quantity, here the volume of alcohol in litres.

Given Data / Assumptions:

• Initial ratio of alcohol : water = 4 : 3.
• A certain base quantity corresponds to these ratio parts.
• 5 litres of water are added to the mixture.
• After addition, the ratio becomes alcohol : water = 4 : 5.
• No alcohol is added or removed, so the quantity of alcohol stays the same.
• We need the volume of alcohol in litres in the original mixture.

Concept / Approach:
When a mixture is described by a ratio, we can express each component as a multiple of a common factor. Let alcohol be 4x litres and water be 3x litres initially. Adding 5 litres of water changes the water quantity but not the alcohol quantity. The new ratio equation then connects 4x and 3x + 5 to 4 : 5. Solving this equation gives x, and hence the amount of alcohol. This method is widely used for ratio based mixture problems.

Step-by-Step Solution:
Let initial alcohol = 4x litres. Let initial water = 3x litres. Total initial mixture = 7x litres. After adding 5 litres of water, water becomes 3x + 5 litres. Alcohol remains 4x litres. New ratio alcohol : water = 4 : 5. So 4x / (3x + 5) = 4 / 5. Cross multiply to get 5 * 4x = 4 * (3x + 5). This simplifies to 20x = 12x + 20. Then 20x − 12x = 20, so 8x = 20, giving x = 2.5. Alcohol quantity = 4x = 4 * 2.5 = 10 litres.

Verification / Alternative check:
Substitute back into the scenario. If x = 2.5, then initial alcohol is 10 litres and initial water is 7.5 litres. After adding 5 litres of water, water becomes 12.5 litres. The new ratio is 10 : 12.5. Dividing both terms by 2.5 gives 4 : 5, which matches the stated new ratio. This confirms that the calculation is correct and that 10 litres of alcohol is consistent with all the given information.

Why Other Options Are Wrong:
Values such as 8 or 12 litres come from incorrect handling of the ratio equation or arithmetic mistakes while simplifying. The larger numbers 18 and 22 litres do not satisfy the new ratio when 5 litres of water are added. Substituting any of these wrong values into the ratio will not produce 4 : 5.

Common Pitfalls:
A frequent mistake is to change both alcohol and water when the problem states that only water is added. Another is misinterpreting the ratio 4 : 5 as meaning a fixed difference rather than a proportional relationship. Carefully setting algebraic expressions for the initial and final situations helps avoid these errors.

Final Answer:
The quantity of alcohol in the original mixture is 10 litres.