If discount of 20% is given on marked price 
of an article then a shopkeeper get the 
profit of 20% what is his Profit% ? if discount 
offered by him changes to 30%.

Let the marked price of the article be denoted by \( M \) and the cost price by \( C \).

### Step 1: Calculate the selling price for a 20% discount
- Discount of 20% on the marked price means the selling price \( S_1 \) when 20% discount is offered is:

\[
S_1 = M - \frac{20}{100} \times M = 0.8M
\]

### Step 2: Calculate the cost price based on profit
- We know that at a 20% discount, the shopkeeper gets a profit of 20%. Hence, the selling price \( S_1 \) is 20% more than the cost price \( C \):

\[
S_1 = C + \frac{20}{100} \times C = 1.2C
\]

- From the above equation:

\[
0.8M = 1.2C
\]

Solving for \( M \) in terms of \( C \):

\[
M = \frac{1.2C}{0.8} = 1.5C
\]

So, the marked price \( M \) is 1.5 times the cost price.

### Step 3: Calculate the selling price for a 30% discount
- Now, when the shopkeeper offers a 30% discount, the selling price \( S_2 \) is:

\[
S_2 = M - \frac{30}{100} \times M = 0.7M
\]

Substitute \( M = 1.5C \) into the equation:

\[
S_2 = 0.7 \times 1.5C = 1.05C
\]

### Step 4: Calculate the new profit percentage
- The profit when offering a 30% discount is the difference between the selling price \( S_2 \) and the cost price \( C \):

\[
\text{Profit} = S_2 - C = 1.05C - C = 0.05C
\]

- The profit percentage is:

\[
\text{Profit \%} = \frac{0.05C}{C} \times 100 = 5\%
\]

### Conclusion:
When the discount increases to 30%, the shopkeeper's profit percentage reduces to **5%**.

Would you like more details or have any questions? 

Here are 5 related questions:
1. How do you calculate profit percentage from selling price and cost price?
2. What happens to profit if the discount is increased further?
3. Can profit still be positive if the discount exceeds 50%?
4. How does markup on cost price affect profit?
5. What is the impact of a discount on customer purchasing behavior?

**Tip:** Always check if the profit percentage formula relates directly to the selling price and cost price for accurate results.

If discount of 20% is given on marked price of an article then a shopkeeper gets the profit of 20%. What is his Profit% if discount offered by him changes to 30%?

Explore how to calculate the profit percentage when a shopkeeper offers a discount of 20% or 30%. This step-by-step solution demonstrates the relationship between discount, selling price, and profit percentage, using key mathematical concepts like percentage and discount calculation.

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