A shopkeeper marks his goods 40 percent above cost price and then allows a discount of 25 percent on the marked price. What is his overall percentage gain?

Introduction / Context:
This is another markup and discount combination problem. The task is to find the net profit or loss percentage when goods are marked up from cost and then sold after a percentage discount on the marked price.

Given Data / Assumptions:

• Goods are marked 40 percent above cost price.
• A discount of 25 percent is given on the marked price.
• We assume no other expenses.
• We must find the overall gain percentage.

Concept / Approach:
First use a convenient assumed cost price and calculate the marked price using the markup. Then apply the discount to find the selling price. Profit is selling price minus cost price, and gain percentage is profit divided by cost price multiplied by 100.

Step-by-Step Solution:
Let cost price (CP) = 100 units.Marked price (MP) = 100 + 40 percent of 100 = 100 + 40 = 140 units.Discount of 25 percent on marked price = 25 percent of 140 = 35 units.Selling price (SP) = MP - discount = 140 - 35 = 105 units.Profit = SP - CP = 105 - 100 = 5 units.Gain percentage = (profit / CP) * 100 = (5 / 100) * 100 = 5 percent.

Verification / Alternative check:
If cost price were Rs. 200 instead, marked price would be Rs. 280. A 25 percent discount reduces this to Rs. 210. Profit = 210 - 200 = 10, which is again 5 percent of 200. So the result is independent of the chosen cost price, confirming 5 percent gain.

Why Other Options Are Wrong:
Values like 10 percent, 15 percent or 20 percent result from incorrect combination of percentages, often by direct subtraction or adding discounts and markups. These do not match the actual difference between selling price and cost price obtained by correct computation.

Common Pitfalls:
A very common error is to subtract the discount percentage directly from the markup percentage and conclude 15 percent profit. This ignores that markup is on cost while discount is on marked price. Always convert percentages into actual rupee or unit figures before combining them.

Final Answer:
The shopkeeper makes an overall gain of 5 percent.