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John ordered 4 pairs of black socks and some additional pair of blue

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Bunuel
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John ordered 4 pairs of black socks and some additional pair of blue [#permalink] New post   14 Mar 2019, 23:52
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Question Stats:

68% (02:51) correct 32% (02:45) wrong based on 44 sessions
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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
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gyanamaya
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Re: John ordered 4 pairs of black socks and some additional pair of blue [#permalink] New post   15 Mar 2019, 00:09
Correct answer is C.
Using hit and trials

Posted from my mobile device
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medic19
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Re: John ordered 4 pairs of black socks and some additional pair of blue [#permalink] New post   15 Mar 2019, 00:40
For the purpose of exam technique: Can set up a table for (where Bla. is Black, Blu. is Blue, Q. is Quantum, P. is Price, T. is Total and Rev. T is Reverse Total

.......Q......P......T.....Rev.T
Bla...4.....2(2)..16....4
Blu...1.....2......2......8
T....................18....12

Luckily A fits in but we need to remember that we need the original or reversed.

Answer is C.
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Re: John ordered 4 pairs of black socks and some additional pair of blue [#permalink] New post   17 Mar 2019, 19:27
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Bunuel wrote:
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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John ordered 4 pairs of black socks and some additional pair of blue [#permalink] New post   22 Mar 2021, 07:47
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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John ordered 4 pairs of black socks and some additional pair of blue [#permalink]
22 Mar 2021, 07:47
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