A shopkeeper marks up his wares by 125% over cost price and then offers a discount of 25% on this marked price.\nIf the cost price of an article is Rs 640, what will be the final selling price (in rupees) after applying both the markup and the discount?

Introduction / Context:
This question is another example of combining a markup with a discount. The trader first increases the price by a large percentage over the cost and later reduces that higher price by a discount before selling to the customer. The net effect is a certain profit percentage on the original cost price. Problems like these are standard in profit and loss sections because they model how retailers use marked prices and discounts to manage profits while making offers appear attractive.

Given Data / Assumptions:

• Cost price (CP) of the article = Rs 640.
• Markup on cost price = 125%.
• Discount on marked price = 25%.
• We must find the final selling price after both steps.
• No taxes or additional fees are mentioned, so we ignore them.

Concept / Approach:
A markup of 125% means the marked price is the cost price plus 125% of the cost price, which is 2.25 times the cost. A discount of 25% means that the customer pays 75% of the marked price. Thus, we can use a multiplier of 2.25 for the markup and then 0.75 for the discount. The final price is the product of the cost price and these two multipliers. This multiplicative viewpoint captures the combined effect of successive percentage changes accurately.

Step-by-Step Solution:
Step 1: Cost price (CP) = Rs 640. Step 2: Markup rate = 125% on cost. Markup factor = 1 + 125 / 100 = 2.25. Step 3: Marked price (MP) = CP * 2.25 = 640 * 2.25. Step 4: Compute 640 * 2.25. This is 640 * (9 / 4) = (640 / 4) * 9 = 160 * 9 = 1440. Step 5: Discount rate = 25% on the marked price. After discount, the customer pays 75% of MP, so factor = 0.75. Step 6: Selling price (SP) = MP * 0.75 = 1440 * 0.75. Step 7: Compute 1440 * 0.75 = 1440 * (3 / 4) = 1080. Step 8: Therefore, the final selling price is Rs 1080.

Verification / Alternative check:
We can compute the net effect on the cost price directly. The combined multiplier is 2.25 (markup) times 0.75 (discount). Multiplying 2.25 by 0.75 gives 1.6875. Thus the final selling price is 1.6875 times the cost price. Applying this to the cost price, SP = 1.6875 * 640 = 1080. This confirms our earlier calculation and shows that the net result is a profit of 68.75% on the original cost price, which is significant even after offering a 25% discount on the marked price.

Why Other Options Are Wrong:
A selling price of Rs 1000 would correspond to a lower net multiplier and thus a smaller profit percentage than implied by the given markup and discount. A price of Rs 920 is even lower and would represent only a modest margin above cost. A price of Rs 860 is barely more than the cost of 640 plus a small extra, which does not align with the large markup followed by a moderate discount. Only Rs 1080 fits the correct calculation for both steps combined.

Common Pitfalls:
Some students may subtract the percentages directly, for example taking 125% minus 25% to get 100%, and then incorrectly concluding that the selling price equals twice the cost price. Others may apply the discount to the cost price rather than to the marked price. To handle such problems safely, always compute the marked price from the cost price with the markup factor, then apply the discount factor to the marked price only, keeping track of each step clearly.

Final Answer:
The selling price of the article after a 125% markup and a 25% discount is Rs 1080.