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Bunuel
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Bunuel
John ordered 4 pairs of black socks and some additional pair of blue socks. The price of the black socks per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of the two colors had been interchanged. This increased the bill by 50%. The ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order was:


(A) 4:1

(B) 2:1

(C) 1:4

(D) 1:2

(E) 1:8

Let price of Black Socks be P and Let price of Blue Socks be Q.

So from question we know, P = 2Q ----- (1)

Let 'x' be the number of Blue socks ordered.

So we can formulate equation(s) in the below way,

Expected Bill (Original Bill) = 4P + xQ ----- (2)
Interchange Bill (Final Bill) = 4Q + xP ----- (3)

Now, we know from question

Interchange Bill (Final Bill) = 1.5 * Expected Bill (Original Bill) ------- (4)

From (2), (3) and (4)

4Q + xP = 1.5 [4P + xQ] ----- (5)

From (1) and (5),

4Q + 2xQ = 1.5 [8Q + xQ]

On solving, we get

x = 16,

So original ratio becomes,

Count of Black : Count of Blue = 4 : 16 OR 4 : 1
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Hi,

For this question, I decided to set prices : as the price of a black pair = 2* the price of a blue pair, let's set the black socks at 20$ and the blue socks at 10$

Our total price is 20*4 pairs + 10*x pairs = 80+10x
however, our quantities were switched and we got: 20x+40

The mistake resulted in 150/100 (or 3/2) of the original price, let's set up the equation to find x:
20x+40=3/2 *(80+10x)
20x+40=120+15x
5x=80
x=16

x is our number of blue pairs and 4 the number of black pairs
Black:Blue = 4:16 = 1:4

Answer C)
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