If a seller gives a discount of 15 % on retail price, she still makes a profit of 2 %. Which of the following ensures that she makes a profit of 20%? Option 1: Give a discount of 5% on retail price Option 2: Give a discount of 2% on retail price Option 3: Increase the retail price by 2% Option 4: Sell at retail price

Answer: Sell at retail price. Solution: We start by understanding what's happening here. A seller has a retail price (the marked price), gives a 15% discount, and still makes a 2% profit. We need to find what she should do to make a 20% profit. Key insight: When dealing with percentages in profit problems, it's smart to assume a convenient number. We assume the retail price is 100 (this makes all calculations super easy). Retail price = 100 Discount = 15% of retail price Discount = 15% × 100 = 15 Selling price = Retail price - Discount Selling price = 100 - 15 = 85 Here's where it gets interesting. We know that even after giving the discount, she makes a 2% profit. Important concept: Profit % = (Selling Price - Cost Price)/(Cost Price) x 100 This means: Selling Price = Cost Price × (1 + Profit%/100) Since she makes 2% profit: 85 = Cost Price × (1 + 2/100) 85 = Cost Price × 1.02 Therefore: Cost Price = 85/1.02 = (85 x 100)/102 = 8500/102 = 500/6 Note: We can simplify this fraction, but keeping it as 500/6 makes the next calculation cleaner. For 20% profit, the selling price should be: Required Selling Price = Cost Price × (1 + 20/100) Required Selling Price = Cost Price × 1.2 Substituting our cost price: Required Selling Price = 500/6 x 1.2 = (500 x 1.2)/6 = 600/6 = 100 The required selling price for 20% profit is 100, which is exactly equal to the retail price! Therefore: To make a 20% profit, the seller should sell at the retail price (without giving any discount). We can think about it logically. Currently with 15% discount she gets 2% profit. For the target of 0% discount she gets 20% profit. By removing the 15% discount, she increases her selling price significantly, which naturally increases her profit from 2% to 20%. Answer: The seller must sell at the retail price (give no discount) to ensure 20% profit.

Arithmetic

Profit & Loss

Medium

If a seller gives a discount of $15 \%$ on retail price, she still makes a profit of $2 \%$ . Which of the following ensures that she makes a profit of $20\%$ ?

Give a discount of $5\%$ on retail price

Give a discount of $2\%$ on retail price

Increase the retail price by $2\%$

Sell at retail price

✅ Correct Option: 4

We start by understanding what's happening here. A seller has a retail price (the marked price), gives a 15% discount, and still makes a 2% profit. We need to find what she should do to make a 20% profit.

Key insight: When dealing with percentages in profit problems, it's smart to assume a convenient number. We assume the retail price is 100 (this makes all calculations super easy).

Retail price = 100

Discount = 15% of retail price

Discount = 15% × 100 = 15

Selling price = Retail price - Discount

Selling price = 100 - 15 = 85

Here's where it gets interesting. We know that even after giving the discount, she makes a 2% profit.

Important concept: Profit % = $\dfrac{\text{Selling Price - Cost Price}}{\text{Cost Price}} \times 100$

This means: Selling Price = Cost Price × (1 + Profit%/100)

Since she makes 2% profit:

85 = Cost Price × (1 + 2/100)

85 = Cost Price × 1.02

Therefore:

Cost Price = $\dfrac{85}{1.02}$

$= \dfrac{85 \times 100}{102}$

$= \dfrac{8500}{102}$

$= \dfrac{500}{6}$

Note: We can simplify this fraction, but keeping it as $\dfrac{500}{6}$ makes the next calculation cleaner.

For 20% profit, the selling price should be:

Required Selling Price = Cost Price × (1 + 20/100)

Required Selling Price = Cost Price × 1.2

Substituting our cost price:

Required Selling Price = $\dfrac{500}{6} \times 1.2$

$= \dfrac{500 \times 1.2}{6}$

$= \dfrac{600}{6}$

$= 100$

The required selling price for 20% profit is 100, which is exactly equal to the retail price!

Therefore: To make a 20% profit, the seller should sell at the retail price (without giving any discount).

We can think about it logically. Currently with 15% discount she gets 2% profit. For the target of 0% discount she gets 20% profit.

By removing the 15% discount, she increases her selling price significantly, which naturally increases her profit from 2% to 20%.

Answer: The seller must sell at the retail price (give no discount) to ensure 20% profit.

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If a seller gives a discount of 15%15 \%15% on retail price, she still makes a profit of 2%2 \%2%. Which of the following ensures that she makes a profit of 20%20\%20%?

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If a seller gives a discount of $15 \%$ on retail price, she still makes a profit of $2 \%$ . Which of the following ensures that she makes a profit of $20\%$ ?