A merchant buys 25 litres of milk every day at Rs 12 per litre. He then mixes 5 litres of water, which is free, and sells the entire 30 litre mixture at Rs 10.40 per litre. What is his overall gain or loss percentage on this transaction?

Introduction / Context:
This question involves a classic case of mixing water with milk to increase profit. Milk is purchased at a cost, water is free, and the mixture is sold at a single uniform rate. The trick is that although the selling price per litre may be lower than the buying price per litre, the addition of free water can still produce an overall profit.

Given Data / Assumptions:
- Milk bought = 25 litres at Rs 12 per litre. - Water mixed = 5 litres, cost assumed to be zero. - Total mixture = 30 litres. - Selling price of mixture = Rs 10.40 per litre. - No wastage occurs and the entire mixture is sold.

Concept / Approach:
We first compute the total cost price of the mixture, which is simply the cost of milk since water is free. Then we compute the total selling price by multiplying the mixture quantity by the selling price per litre. Finally, we compare total selling price with total cost price to obtain profit and profit percentage.

Step-by-Step Solution:
Step 1: Cost of 25 litres of milk = 25 * 12 = Rs 300. Step 2: Water is free, so total cost price C = Rs 300. Step 3: Total quantity after mixing = 25 + 5 = 30 litres. Step 4: Total selling price S = 30 * 10.40 = Rs 312. Step 5: Profit = S - C = 312 - 300 = Rs 12. Step 6: Profit percent = (12 / 300) * 100 = 4%.

Verification / Alternative check:
We can compute effective selling price per litre in terms of cost. Total cost is 300 for 30 litres, which means effective cost per litre of mixture is 300 / 30 = Rs 10. The merchant actually charges Rs 10.40 per litre, which is 0.40 more than effective cost. Extra 0.40 on base 10 is 4%, confirming the profit percentage is 4% on cost price.

Why Other Options Are Wrong:
Option 8% profit would require a profit double of what is actually earned. Option 2% profit and 6% profit correspond to total selling prices that do not match the given rate of Rs 10.40 per litre when applied to 30 litres. Only 4% keeps both cost and given selling price consistent.

Common Pitfalls:
One common mistake is to compare 12 and 10.40 directly and assume a loss because the selling price per litre appears less than the purchase price per litre. This ignores the effect of free water. Another error is to forget to multiply by the total number of litres when computing total selling price. Always work with totals when mixture is involved.

Final Answer:
The merchant makes a 4% profit on the transaction.