The sale price of an article including sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12% on the cost price (before tax), what is the cost price of the article?

Introduction / Context:
This problem combines the concepts of profit and sales tax. The final amount paid by the customer includes tax on the selling price, while the shopkeeper's profit is calculated on the cost price. We are asked to reverse these steps and find the original cost price given the total bill and the tax and profit percentages.

Given Data / Assumptions:

• Total amount paid by the customer (selling price plus sales tax) = Rs. 616.
• Sales tax rate = 10% of the shopkeeper's selling price before tax.
• Shopkeeper's profit on cost price = 12%.
• We must find the cost price of the article.

Concept / Approach:
Let CP be the cost price and SP be the selling price before adding tax. The shopkeeper makes a 12% profit, so SP = 1.12 * CP. Sales tax is 10% of SP, so the tax amount = 0.10 * SP, and the total amount paid by the customer is SP + 0.10 * SP = 1.10 * SP. This total is given as Rs. 616. We first find SP from this relation, then use SP = 1.12 * CP to recover CP.

Step-by-Step Solution:
Step 1: Let cost price be CP, selling price before tax be SP.Step 2: Given profit of 12%, SP = 1.12 * CP.Step 3: Sales tax at 10% means total amount paid = SP + 0.10 * SP = 1.10 * SP.Step 4: Given that 1.10 * SP = Rs. 616.Step 5: Therefore SP = 616 / 1.10 = Rs. 560.Step 6: Now SP = 1.12 * CP implies CP = SP / 1.12 = 560 / 1.12.Step 7: Compute CP: 1.12 = 112 / 100, so CP = 560 * 100 / 112 = 56000 / 112 = Rs. 500.

Verification / Alternative check:
With CP = Rs. 500, profit at 12% gives SP = 500 * 1.12 = Rs. 560.Sales tax at 10% on SP = 0.10 * 560 = Rs. 56.Total amount paid by customer = 560 + 56 = Rs. 616, which matches the figure in the question.

Why Other Options Are Wrong:
If CP were Rs. 560, SP at 12% profit would be larger than 560 and 10% tax on that would exceed Rs. 616. Values like Rs. 530, Rs. 514 or Rs. 480 similarly fail to produce a total of exactly Rs. 616 when 12% profit and 10% tax are correctly applied. Only CP = Rs. 500 passes the reverse calculation test.

Common Pitfalls:
Some learners mistakenly apply the 10% sales tax directly on the cost price instead of on the selling price. Others confuse profit percentage and tax percentage, adding or subtracting 10 and 12 directly from 616 without proper structure. Keeping track of the sequence (cost to selling price to taxed price) and basing each percentage on the correct amount is essential.

Final Answer:
The cost price of the article is Rs. 500.