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

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

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New post 14 Mar 2019, 23:52
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

45% (03:20) correct 55% (02:03) wrong based on 11 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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Re: John ordered 4 pairs of black socks and some additional pair of blue  [#permalink]

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New post 15 Mar 2019, 00:09
Correct answer is C.
Using hit and trials

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Re: John ordered 4 pairs of black socks and some additional pair of blue  [#permalink]

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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]

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

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