A sells an article to B at a profit of 20%, B sells it to C at a loss of 25% and C sells it to D at a profit of 40%; if D pays Rs. 252 for the article, how much did A originally pay for it?

Introduction / Context:
This chained profit and loss question follows an article as it is sold through several people, each making a gain or loss at different percentages. Starting from the final selling price paid by D, we need to work backwards through the percentage changes to recover the original cost price paid by A. This type of question is common in aptitude tests, where it develops an understanding of forward and backward percentage calculations.

Given Data / Assumptions:

• A sells the article to B with a profit of 20% over A cost price.
• B sells to C at a loss of 25% with respect to B cost.
• C sells to D at a profit of 40% over C cost.
• Final price paid by D = Rs. 252.
• We need to find the amount originally paid by A, which is the initial cost price.

Concept / Approach:
Backward percentage calculation is best handled by reversing each change step by step. When we know a selling price and a profit percentage, the cost price is given by selling price divided by (1 + profit percentage / 100). When there is a loss, cost price is selling price divided by (1 - loss percentage / 100). Here we start from D price, compute the price at which C bought the article, then the price B paid, and finally the original price A paid. This method ensures clarity at every stage.

Step-by-Step Solution:
Step 1: Let the price at which C sells the article to D be denoted as SP_CD = Rs. 252.Step 2: C makes a profit of 40% when selling to D.Step 3: So SP_CD = Cost price for C * (1 + 40 / 100) = Cost price for C * 1.4.Step 4: Cost price for C = 252 / 1.4 = Rs. 180.Step 5: Therefore, B sells the article to C for Rs. 180.Step 6: B sells at a loss of 25% to C.Step 7: Thus 180 = Cost price for B * (1 - 25 / 100) = Cost price for B * 0.75.Step 8: Cost price for B = 180 / 0.75 = Rs. 240.Step 9: Therefore, A sells the article to B for Rs. 240.Step 10: A made a profit of 20% when selling to B.Step 11: So 240 = Cost price for A * 1.2.Step 12: Cost price for A = 240 / 1.2 = Rs. 200.

Verification / Alternative check:
We can verify by moving forward from A cost price. If A cost price is Rs. 200, A sells to B at 20% profit, so B pays 200 * 1.2 = Rs. 240. B incurs a 25% loss when selling to C, so C pays 240 * 0.75 = Rs. 180. C then sells to D at 40% profit, so D pays 180 * 1.4 = Rs. 252. The forward chain exactly reproduces the given final price, confirming that the initial cost of Rs. 200 is correct.

Why Other Options Are Wrong:

• Rs. 196: This is close to Rs. 200 but does not match the percentage transformations when checked forward.
• Rs. 210 and Rs. 235: These values do not lead to a final price of Rs. 252 when the given profit and loss percentages are applied in sequence.

Common Pitfalls:

• Applying the percentage operations in the wrong direction, for example multiplying instead of dividing when working backwards.
• Mixing up profit and loss formulas and using 1 + percentage for both cases.
• Rounding values too early, especially when dealing with fractional costs, which can lead to slight but important errors in later steps.

Final Answer:
A originally paid Rs. 200 for the article before it passed through B and C to D.