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A clothing retailer bought 2 shipments of equal numbers of dresses at

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A clothing retailer bought 2 shipments of equal numbers of dresses at [#permalink]

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New post 12 Dec 2017, 23:20
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CHALLENGE QUESTION:



A clothing retailer bought 2 shipments of equal numbers of dresses at the same price. When the first shipment was sold in its entirety at $70 per dress, it generated $1,600 in profits. When the retailer sold the second shipment in its entirety at $90 per dress, it generated $2,400 in profits. What was the total number of dresses in both shipments?

(A) 40
(B) 50
(C) 60
(D) 80
(E) 100
[Reveal] Spoiler: OA

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A clothing retailer bought 2 shipments of equal numbers of dresses at [#permalink]

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New post 12 Dec 2017, 23:56
Lets say there were x number of dresses in each shipment. And cost of the each dress is y. Then we can set up following equation:

70x - xy = 1600
90x -xy = 2400


20x = 800

x= 40

Therefore there are 80 dresses in both shipments

Last edited by kablayi on 13 Dec 2017, 04:32, edited 1 time in total.

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Re: A clothing retailer bought 2 shipments of equal numbers of dresses at [#permalink]

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New post 13 Dec 2017, 04:22
Two shipments equal number of dress, Let dress be x , y be the price of each dress
1. Given 70x = 1600 + xy
2. Given 90x =2400+xy

(note 1600 and 2400 is the profit) Equate with xy
90x-2400=70x-1600
20x =800
x= 40

The question is total number of shpments, so it is 40+40 = 80

Ans : D

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Re: A clothing retailer bought 2 shipments of equal numbers of dresses at [#permalink]

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New post 14 Dec 2017, 01:28
Bunuel wrote:

CHALLENGE QUESTION:



A clothing retailer bought 2 shipments of equal numbers of dresses at the same price. When the first shipment was sold in its entirety at $70 per dress, it generated $1,600 in profits. When the retailer sold the second shipment in its entirety at $90 per dress, it generated $2,400 in profits. What was the total number of dresses in both shipments?

(A) 40
(B) 50
(C) 60
(D) 80
(E) 100


Dresses in Shipment 1 = S1 = n
Dresses in Shipment 2 = S2 = n

Cost per shipment = C

Profit = Revnune - Cost

For S1: 1600 = 70n - C

For S2: 2400 = 90n - C

Note: The cost of both shipments is the same as both shipment are identical of terms of number and cost per dress.

Subtract equations

800 = 20n...........n =40 dress per shipment

Then Toyla shipment = 80 dresses

Answer: D

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A clothing retailer bought 2 shipments of equal numbers of dresses at [#permalink]

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New post 14 Dec 2017, 02:47
Bunuel wrote:

CHALLENGE QUESTION:



A clothing retailer bought 2 shipments of equal numbers of dresses at the same price. When the first shipment was sold in its entirety at $70 per dress, it generated $1,600 in profits. When the retailer sold the second shipment in its entirety at $90 per dress, it generated $2,400 in profits. What was the total number of dresses in both shipments?

(A) 40
(B) 50
(C) 60
(D) 80
(E) 100


Since the number of dresses and cost price is the same in both,
Simply note that an extra $20 charge ($90 sale price instead of $70 sale price) led to an extra profit of $800 (= 2400 - 1600).
So there must have been 800/20 = 40 dresses in one lot.
This means a total of 80 dresses.

Answer (D)
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A clothing retailer bought 2 shipments of equal numbers of dresses at [#permalink]

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New post 14 Dec 2017, 11:14
Let No. of dresses be n and original cost per dress be x

Then 70n=x+1600
90n=x+2400

Solving gives n=40

Thus total dresses is 2n=80

Ans:D

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A clothing retailer bought 2 shipments of equal numbers of dresses at   [#permalink] 14 Dec 2017, 11:14
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