To solve this problem, let’s break down the steps:

Step 1: Calculate the Sale Price after Discounts

Let the List Price (LP) of the shirt be $x$.

1. The first discount is 40%, so the price after the first discount is: $x \times (1 - 0.4) = 0.6x$

2. The second discount is 30% on the new price, so the final sale price after both discounts is: $0.6x \times (1 - 0.3) = 0.6x \times 0.7 = 0.42x$

Step 2: Determine the Cost Price

Lee Cooper earns a profit of 5% on this sale. Let the cost price (CP) of the shirt be $y$.

Since the sale price after discounts gives a 5% profit: $0.42x = 1.05y$ From this, we can express $y$ in terms of $x$: $y = \frac{0.42x}{1.05} = 0.4x$

Step 3: Calculate the Desired Sale Price for 50% Profit

Now, to earn a profit of 50%, the sale price needs to be: $1.5y = 1.5 \times 0.4x = 0.6x$

Step 4: Determine the Appropriate Discount on the List Price

We need to find the discount that will result in a sale price of $0.6x$:

• Selling at LP means selling at $x$.
• Selling at a 40% discount means $0.6x$, which matches our target.

Answer:

The correct answer is:

• Sell at 40% discount on LP.

Would you like further details or have any questions about this solution?

---

Here are five related questions to explore further:

1. What would be the required discount to earn a profit of 60% instead of 50%?
2. How would the solution change if Lee Cooper had to give three successive discounts instead of two?
3. What is the cost price if the profit was to be 10% after the two discounts?
4. What happens if Lee Cooper applies a single discount equivalent to the two successive discounts?
5. How would a change in list price affect the discount percentages?

Tip: Successive discounts can be calculated by multiplying their respective remaining percentages (e.g., $(1 - 0.4) \times (1 - 0.3)$ for 40% and 30% discounts).