Problem Solving

AAPL wrote:Veritas Prep

When sold at a 40% discount, a sweater nets the merchant a 20% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?

A. 20%
B. 40%
C. 50%
D. 80%
E. 100%

OA E

Let's work BACKWARDS.

Let's say the WHOLESALE price was $100

the merchant made a net profit of 20% on the wholesale cost (which was $100)
So, the merchant sold the sweater for $120

[the sweater] sold at a 40% discount
Let M = the markup price on the label (before any discounts).
So, 40% less than M = $120
In other words, 60% of M = $120
Or we can write 0.6M = 120
So, M = 200
In other words, the markup price (before any discounts) was $200

If the wholesale price was $100, and the markup price was $200, then the sweater was originally marked up by 100%

Answer: E

Cheers,
Brent

AAPL wrote:Veritas Prep

When sold at a 40% discount, a sweater nets the merchant a 20% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?

A. 20%
B. 40%
C. 50%
D. 80%
E. 100%

OA E

Say the cost price = $x and the markup price = $y.

After the discount of 40%, the selling price = (1 - 40%) of y = 0.6y

Profit = 20% of x = 0.2x

Thus, Selling price - Cost price = Profit

0.6y - x = 0.2x

y = 2x

y = 200% of x

The sweater is marked up by 100% from wholesale at its normal retail price.

The correct answer: E

Hope this helps!

-Jay
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AAPL wrote:Veritas Prep

When sold at a 40% discount, a sweater nets the merchant a 20% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?

A. 20%
B. 40%
C. 50%
D. 80%
E. 100%

OA E

We can let the discount price of the sweater be $60. So the normal retail price is $100. Now we can let n = the wholesale cost, we have:

1.2n = 60

n = 60/1.2 = 50

So the wholesale cost is $50 and the sweater must have been marked up by $50 or 100% of its wholesale cost to get to its normal retail price of $100.

Answer: E