A shopkeeper marks up the cost price of his goods by 60% and then offers a discount of 25% on the marked price.\nIf the cost price of an article is Rs 1600, what will be the final selling price (in rupees) after applying both the markup and the discount?

Introduction / Context:
This question involves both markup and discount, a very common pattern in profit and loss problems. First the trader increases the price above cost by a given percentage to determine the marked price. Later, to attract customers, a percentage discount is applied to that marked price. The net effect on the selling price depends on both percentages and cannot be obtained by simply adding or subtracting them. Understanding how to handle such successive percentage changes is essential for solving real life pricing and sales questions.

Given Data / Assumptions:

• Cost price (CP) of the article = Rs 1600.
• Markup rate on cost price = 60%.
• Discount rate on marked price = 25%.
• We need to find the final selling price after both steps.
• All prices and percentages are applied in the normal arithmetic way.

Concept / Approach:
The strategy is to proceed in two stages. First compute the marked price by increasing the cost price by 60%. Then compute the selling price by reducing the marked price by 25%. Mathematically this is done by multiplying the cost price by (1 plus markup rate expressed as a decimal) and then multiplying the resulting marked price by (1 minus discount rate expressed as a decimal). This avoids any confusion and shows clearly how successive percentage changes combine through multiplication rather than simple addition or subtraction.

Step-by-Step Solution:
Step 1: Cost price (CP) = Rs 1600. Step 2: Markup rate = 60%, so factor for markup = 1 + 60 / 100 = 1.6. Step 3: Marked price (MP) = CP * 1.6 = 1600 * 1.6 = Rs 2560. Step 4: Discount rate on marked price = 25%, so discount factor = 1 - 25 / 100 = 0.75. Step 5: Selling price (SP) = MP * 0.75 = 2560 * 0.75. Step 6: Calculate 2560 * 0.75. This is the same as 2560 * 3 / 4 = 1920. Step 7: Therefore the final selling price after markup and discount is Rs 1920.

Verification / Alternative check:
We may also combine both percentage effects into one factor. The net multiplier on cost price is (1 + 0.60) * (1 - 0.25) = 1.6 * 0.75. Multiply these to get 1.6 * 0.75 = 1.20. Thus the effective effect on cost is a 20% increase overall, and SP = 1.20 * 1600 = 1920. This cross check confirms that the detailed stepwise approach and the combined factor approach give the same answer, so the computation is consistent.

Why Other Options Are Wrong:
If the selling price were Rs 2000, that would correspond to a different effective net increase on cost price, not exactly 20%. A value of Rs 2120 implies an even larger overall percentage, which does not match a 60% markup followed by a 25% discount. A price of Rs 2200 is higher still and does not satisfy the computed multiplier of 1.20. Only Rs 1920 is consistent with a 60% increase followed by a 25% reduction on the marked amount.

Common Pitfalls:
A common mistake is to subtract the discount rate from the markup rate directly, for example saying 60% minus 25% equals 35% and applying that to the cost, which is incorrect because the discount applies to the increased marked price, not the original cost. Others may misapply the discount to the cost price instead of the marked price. Always remember that each percentage change acts on the current value at that stage, and successive changes combine multiplicatively, not by simple addition or subtraction.

Final Answer:
The final selling price of the article is Rs 1920.