Let the marked price be M and the cost price be C.

Step 1: Understanding the First Scenario

• Discount given = 30%
  $\text{Selling Price} = M - 30\% \text{ of } M = 0.7M$
• Profit is 26%, meaning: $0.7M = 1.26C$

Step 2: Understanding the Second Scenario

• The discount is reduced by 33.33%, meaning the new discount is: $30\% - \left( 33.33\% \times 30\% \right) = 30\% - 10\% = 20\%$
• New Selling Price: $\text{New } S.P = M - 20\% \text{ of } M = 0.8M$
• Substituting $M$ from $0.7M = 1.26C$: $M = \frac{1.26C}{0.7} = 1.8C$
• New Selling Price: $S.P = 0.8 \times 1.8C = 1.44C$
• New Profit %: $\text{Profit} = \frac{S.P - C.P}{C.P} \times 100$ $= \frac{1.44C - C}{C} \times 100$ $= \frac{0.44C}{C} \times 100 = 44\%$

Final Answer:

The approximate new profit percentage is 44%.

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Do you want a more detailed breakdown or a different approach? Here are some related questions:

1. How does the relationship between cost price, selling price, and marked price affect discounts and profits?
2. What happens if the discount is further reduced to 10%?
3. How can we generalize this method for any given discount and profit percentage?
4. How do markdown strategies affect revenue and overall profit margins?
5. What would be the loss percentage if the discount increased instead of decreasing?

Tip: Always express percentage reductions in absolute terms before applying changes to avoid confusion in calculations.