In a festive scheme, a pack of three soaps with marked price Rs. 45 is sold for Rs. 42 and still gives the shopkeeper a profit of 5%; what is the cost price of the entire three-soap pack?

Introduction / Context:
This question focuses on calculating cost price when selling price and profit percentage are known. The situation describes a promotional scheme where a pack of three soaps with a marked price is sold at a slightly reduced price, yet the shopkeeper still earns a profit. This type of problem is very common in commerce and aptitude tests, helping candidates understand the relationship between marked price, selling price, cost price and profit percentage.

Given Data / Assumptions:

• Marked price of a pack of three soaps = Rs. 45.
• Selling price of the pack in the scheme = Rs. 42.
• Profit made by selling at Rs. 42 is 5% of the cost price.
• We assume no other additional charges or taxes.
• We are required to find the cost price of the entire three-soap pack.

Concept / Approach:
The key formula in profit and loss is: Selling price = Cost price * (1 + profit percentage / 100) when there is a profit. Here, we know the selling price and the profit percentage, so we can invert the formula to find the cost price. That is, Cost price = Selling price / (1 + profit percentage / 100). We do not actually need to use the marked price numerically, because the question directly connects profit to cost price and the given selling price of Rs. 42.

Step-by-Step Solution:
Step 1: Let the cost price of the pack be denoted by CP.Step 2: Profit percentage = 5%.Step 3: Selling price of the pack = Rs. 42.Step 4: Relation for profit: Selling price = Cost price * (1 + 5 / 100).Step 5: That means 42 = CP * 1.05.Step 6: So CP = 42 / 1.05.Step 7: Compute 42 / 1.05 = 4000 / 100 = Rs. 40 exactly.Step 8: Therefore, the cost price of the three-soap pack is Rs. 40.

Verification / Alternative check:
We can verify by calculating the profit once we assume cost price is Rs. 40. If CP = Rs. 40 and SP = Rs. 42, profit = 42 minus 40 = Rs. 2. Profit percentage = (2 / 40) * 100 = 5%. This exactly matches the given profit percentage. The marked price of Rs. 45 simply indicates that the shopkeeper is offering a Rs. 3 discount off the marked price, but the core calculations still satisfy the required profit condition.

Why Other Options Are Wrong:

• Rs. 38: At this cost, profit would be 42 minus 38 = Rs. 4, which is more than 5% of 38. The profit percentage would be approximately 10.53%.
• Rs. 39: Profit would be Rs. 3 on cost 39, which is about 7.69%, not 5%.
• Rs. 41: Profit would be Rs. 1 on cost 41, which is about 2.44%, again not equal to 5%.

Common Pitfalls:

• Using marked price instead of selling price in the profit formula and mixing up which value is the base.
• Applying the percentage directly to the selling price rather than to the cost price.
• Performing the division 42 / 1.05 incorrectly and rounding too early, which may lead to a slightly wrong answer.

Final Answer:
The cost price of the three-soap pack that gives a 5% profit when sold for Rs. 42 is Rs. 40.