A specialty beverage distributor purchased a crate of rare botanical spirits at a total co… — GMAT

A specialty beverage distributor purchased a crate of rare botanical spirits at a total cost price of $\$400$ . The distributor marked up the cost price by $50\%$ to establish the regular list price. During a promotional event, the list price was discounted by $x\%$ . If the distributor earned a net profit of $20\%$ on the original cost price of the crate, what is the value of $x$ ?

A
$15$
$20$ Answer
C
$25$
D
$30$
E
$33\frac{1}{3}$

Answer

The value of

x

20

The regular list price is calculated as

1.50 \times \$400 = \$600

. Since the distributor earns a

20\%

profit on the cost price, the discounted selling price must be

1.20 \times \$400 = \$480

. The discount amount is

\$600 - \$480 = \$120

. Expressed as a percentage of the list price,

x = \frac{120}{600} \times 100 = 20

Step-by-Step Solution

Calculate the regular list price based on the

50\%

markup.

List Price =

\$400 \times (1 + 0.50) = \$600

Markup is applied directly to the original cost price.

Determine the actual selling price after the discount using the

20\%

net profit target.

Selling Price =

\$400 \times (1 + 0.20) = \$480

Net profit percentage is calculated relative to the cost price base.

Calculate the dollar discount and express it as a percentage of the list price.

Discount Amount =

\$600 - \$480 = \$120

. Discount Percentage

x\% = \frac{\$120}{\$600} \times 100\% = 20\%

. Thus,

x = 20

Percentage discount is always measured relative to the original list price.

Key Concept

Markup, Profit, and Successive Percentage Discounts

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic