The selling price of a table is Rs. 2808 and the profit percentage is 17%. What is the cost price of the table?

Introduction / Context:
This problem relates selling price, cost price, and profit percentage. In commercial arithmetic, when the profit percentage and selling price are known, we can find the cost price by reversing the percentage increase. Profit is always calculated on the cost price, so the selling price is cost price plus profit. Understanding the direct formula linking these values is essential for quickly solving such questions.

Given Data / Assumptions:
Selling price (SP) of the table = Rs. 2808.
Profit percentage = 17 percent.
Profit is calculated on the cost price (CP).
We are required to find the cost price of the table.

Concept / Approach:
If the profit on cost price is P percent, then selling price = cost price * (1 + P / 100). Here, with a 17 percent profit, we have SP = CP * 1.17. Hence, cost price CP can be obtained by CP = SP / 1.17. This is a direct algebraic rearrangement and avoids any confusion between the various price components. Once we compute CP, we can check by adding 17 percent of CP to see whether we indeed get back the selling price.

Step-by-Step Solution:
Let cost price be CP. Profit percentage = 17 percent, so profit = 17 percent of CP. Thus selling price SP = CP + 0.17 * CP = 1.17 * CP. We are given SP = Rs. 2808. So 1.17 * CP = 2808. Therefore CP = 2808 / 1.17. Compute 2808 / 1.17 = 2400. Hence, the cost price of the table is Rs. 2400.

Verification / Alternative check:
Check by computing profit on the found cost price. Profit = 17 percent of 2400 = 0.17 * 2400 = 408. Add this profit to the cost price: 2400 + 408 = 2808. This matches the given selling price, confirming that our calculated cost price is correct. If we had chosen any other cost price, the resulting selling price after adding 17 percent would not equal 2808.

Why Other Options Are Wrong:
If the cost price were 2288, then SP at 17 percent profit would be 2288 * 1.17, which does not equal 2808. Similarly, 2300 as cost price would generate a selling price different from 2808 when profit is 17 percent. A cost price of 3285 is actually higher than the selling price and cannot yield a 17 percent profit. Only a cost price of 2400 yields the correct selling price when we apply a 17 percent profit margin.

Common Pitfalls:
One common mistake is to compute 17 percent of the selling price instead of the cost price and then subtract, which produces incorrect results because the base for percentage is wrong. Another error involves treating selling price as cost price times (100 / 117) without careful calculation, leading to arithmetic slips. To avoid such problems, always write the fundamental relation SP = CP * (1 + profit percent / 100) and solve explicitly for the unknown variable.

Final Answer:
The cost price of the table is Rs. 2400.