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

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
John ordered 4 pairs of black socks and some additional pair of blue  [#permalink]

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14 Mar 2019, 23:52
00:00

Difficulty:

55% (hard)

Question Stats:

50% (02:49) correct 50% (01:55) wrong based on 14 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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Intern
Joined: 31 Mar 2018
Posts: 5
Re: John ordered 4 pairs of black socks and some additional pair of blue  [#permalink]

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15 Mar 2019, 00:09
Using hit and trials

Posted from my mobile device
Intern
Joined: 17 Sep 2018
Posts: 42
Re: John ordered 4 pairs of black socks and some additional pair of blue  [#permalink]

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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.

Manager
Joined: 11 Mar 2018
Posts: 158
Re: John ordered 4 pairs of black socks and some additional pair of blue  [#permalink]

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17 Mar 2019, 19:27
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
Re: John ordered 4 pairs of black socks and some additional pair of blue   [#permalink] 17 Mar 2019, 19:27
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