A retailer acquires items at a cost of N dollars apiece, sells them on

Question

A retailer acquires items at a cost of N dollars apiece, sells them online at a 40% mark-up, and then pays to ship the items to the buyers. Shipping costs are currently 10% of the selling price of each item, and the retailer incurs no other costs beyond those of acquiring and shipping items. If shipping costs increase to 12% of the selling price of each item, then the retailer's net profit on each sale will decrease by

(A) between 2 and 4 percent
(B) between 4 and 6 percent
(C) between 6 and 8 percent
(D) between 8 and 10 percent
(E) more than 10 percent

(A) between 2 and 4 percent
(B) between 4 and 6 percent
(C) between 6 and 8 percent
(D) between 8 and 10 percent
(E) more than 10 percent

TestPrepUnlimited · Answer

The profit without the shipping cost is  140\%*N - 100\%*N . The shipping price is 10%*N, including that the total profit would be  140\%*N - 100\%*N - 10\%*N = 30%*N .

If the shipping costs increase to 12%, then the total profit would be  30\%*N - 2\%*N = 28\%*N  instead. Thus the decrease is  \frac{2\%*N}{30\%*N} = \frac{1}{15} = \frac{6}{90} > \frac{6}{100} .

Then we know this is a little bigger than 6%, we choose C.

Ans: C

ayushk09 · Answer

As mentioned in Question, shipping price is on selling price rather aquired price. Hence, shipping should be calculated on 140% of N rather 100% of N.
Please correct if i misunderstood

Fdambro294 · Answer

Let N = $100

Selling Price is a 40% markup ——> $140

Shipping costs are 10% of the selling price —-> $14

Original net profit:

$140 - ($114) = $26

Now, shipping costs increase an extra 2% of the selling price (which is still $140)

10% of 140 ———> 14.0

1% of 140 ———-> 1.40

(1.4) * 2 = 2.8

Thus our costs have risen to 116.80

If we boost the costs up to 117, the percentage decrease in gross profit will be an overestimate (cost should be a bit lower so we are making it a little worse than it actually is)

New estimated gross profit = 140 - 117 = $23

Percentage decrease in gross profit ——-> we can look at the fractional decrease

(23 - 26) / 26 =

- (3/26)

A 10% decrease in the original net profit would have represented a decrease (NUM) of -2.6 on and original gross profit of 26

Even with our overestimate of costs, the gross profit decrease is still greater than 10%

E

Greater than 10%

Note: question is asking for the percentage decrease in net profit - not the profit percentage

Posted from my mobile device

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

Crytiocanalyst · Answer

x1 + y1 + z1 = 100 ;........1

x2 + y2 +z2 = 100 ;..........2

x1 +10 = y1 ;...........3
y2 = 5z2 ;....................4

x2 =1.2x1 , y2 =1.2y1 .......5

Solving 1 to 5 we get 
3/26*100 greataer than 10

Therefore IMO E

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A retailer acquires items at a cost of N dollars apiece, sells them on

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A retailer acquires items at a cost of N dollars apiece, sells them on

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