MBA Nexus - CAT & OMETS 2024, [14-10-2024 09:28]
Q1 Lee cooper gives two successive discounts of 40% and 30% on List Price (LP) of a shirt and earns a profit of 5%. At what price should he sell the shirt to earn a profit  of 50%?

MBA Nexus - CAT & OMETS 2024, [14-10-2024 09:30]
[ Poll : Ans ]
- sell at LP
- sell at 40% discount on LP
- sell at 20% discount on LP
- sell at 30% discount on LP

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?

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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).

Lee Cooper gives two successive discounts of 40% and 30% on the List Price (LP) of a shirt and earns a profit of 5%. At what price should he sell the shirt to earn a profit of 50%?

Learn how to calculate the final selling price of a shirt after applying two successive discounts of 40% and 30%, and how Lee Cooper can achieve a 50% profit. Explore key concepts of discount calculation, profit formulas, and algebraic expressions. Suitable for Grades 10-12 students.

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