A milk merchant buys 50 litres of milk at ₹40 per litre and then mixes 5 litres of water into it (water is assumed to have zero cost).\nHe sells the entire milk-water mixture at ₹42 per litre.\nWhat is the merchant's profit percentage on his total cost price?

Introduction:
This question tests profit percentage when free water is added to increase volume. The cost is only for milk, but revenue is earned on the entire mixture volume. We compute total cost, total revenue, profit, and then profit percentage based on cost price.

Given Data / Assumptions:

• Milk bought = 50 litres
• Cost price of milk = ₹40 per litre
• Water added = 5 litres (assume cost = ₹0)
• Selling price of mixture = ₹42 per litre

Concept / Approach:
Total cost = milk litres * CP per litre.\nTotal volume sold = milk + water.\nTotal revenue = total volume * SP per litre.\nProfit% = (profit / cost) * 100.

Step-by-Step Solution:
Total cost = 50 * 40 = 2000Total mixture volume = 50 + 5 = 55 litresTotal revenue = 55 * 42 = 2310Profit = 2310 - 2000 = 310Profit percentage = (310 / 2000) * 100Profit percentage = 15.5%

Verification / Alternative Check:
Effective cost per litre of mixture = total cost / total litres = 2000/55 ≈ 36.36.\nProfit per litre = 42 - 36.36 ≈ 5.64.\nProfit% ≈ (5.64/36.36)*100 ≈ 15.5%, consistent with the direct method.

Why Other Options Are Wrong:
17.2%, 16.6%: overestimates profit, often from dividing by wrong base.14.4% or 12.0%: underestimates profit, typically from using 50 litres in revenue instead of 55.

Common Pitfalls:
Calculating revenue only on 50 litres instead of 55 litres.Taking profit percentage on selling price rather than cost price.Assigning a cost to water when not stated.

Final Answer:
15.5%