Mohit sells a table at a profit of 25%. If he reduces the selling price of the same table by Rs 240, he incurs a loss of 5%. What was the initial selling price of the table, in rupees?

Introduction / Context:
This profit and loss question involves two different selling prices of the same article, with a profit at the higher selling price and a loss at the lower selling price. The objective is to determine the original selling price using both profit and loss conditions. This tests algebraic formulation of profit and loss relationships.

Given Data / Assumptions:

• At the initial selling price, Mohit makes a profit of 25%.
• If he reduces the selling price by Rs 240, he makes a loss of 5% on cost price.
• The cost price of the table is assumed constant in both scenarios.
• We are required to find the initial selling price in rupees.

Concept / Approach:
Let the unknown cost price be CP. First selling price SP1 gives 25% profit, so SP1 = CP * 1.25. Second selling price SP2 gives a loss of 5%, so SP2 = CP * 0.95. We know that SP2 is less than SP1 by Rs 240, so SP1 - SP2 = 240. Substituting in terms of CP gives an equation that can be solved easily for CP and then for SP1.

Step-by-Step Solution:
Let CP = x rupees. Initial selling price SP1 = x * 1.25. Reduced selling price SP2 = x * 0.95. Given SP1 - SP2 = 240, so 1.25x - 0.95x = 240. This simplifies to 0.30x = 240, hence x = 240 / 0.30 = 800 rupees. Now SP1 = 1.25 * 800 = Rs 1000.

Verification / Alternative check:
With CP = Rs 800 and SP1 = Rs 1000, profit = 1000 - 800 = 200 rupees, which is 25% of 800. For SP2, subtract 240 from SP1: 1000 - 240 = 760 rupees. Loss = 800 - 760 = 40 rupees, which is 5% of 800. Both conditions match the given data, confirming that the original selling price is Rs 1000.

Why Other Options Are Wrong:
If SP1 were 800, 1040, or 1120, then either the profit or the loss or the difference of Rs 240 would not be satisfied simultaneously. Only when SP1 is 1000 and CP is 800 do both profit and loss percentages and the Rs 240 difference hold true.

Common Pitfalls:
Many students incorrectly assume CP is 1000 or directly subtract percentages instead of relating them via algebra. Another mistake is to apply the 25% and 5% changes successively to selling price instead of to cost price, which leads to wrong equations.

Final Answer:
The initial selling price of the table was Rs 1000.