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In a shop, 40% socks are white and rest are black. 60% socks are made

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In a shop, 40% socks are white and rest are black. 60% socks are made  [#permalink]

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New post 26 Nov 2019, 00:07
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Question Stats:

56% (02:58) correct 44% (02:44) wrong based on 44 sessions

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In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks are made of cotton?

(A) 100
(B) 80
(C) 60
(D) 50
(E) 25


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In a shop, 40% socks are white and rest are black. 60% socks are made  [#permalink]

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New post Updated on: 26 Nov 2019, 21:25
Let the total number of socks be 20x.
The number of White socks is 8x of which 2x is Cotton and 6x is Wool.
The number of Black socks is 12x of which 20 is Wool and (12x-20) is Cotton.
So the total number of Wool socks is 6x+20 which is equal to 8x (40% of the total number of socks 20x)
6x+20=8x....> x=10
The number of Black Cotton socks is 12x-20=12*10-20=100. ANS: A

Originally posted by effatara on 26 Nov 2019, 05:19.
Last edited by effatara on 26 Nov 2019, 21:25, edited 1 time in total.
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Re: In a shop, 40% socks are white and rest are black. 60% socks are made  [#permalink]

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New post 26 Nov 2019, 12:01
I came about it a different way but let me be sure I got it
20 black wool socks
1/4 the white socks are cotton - 3/4 the white socks are wool
if 20 sock are 1/4 then 60 socks are 3/4 and total 80 socks are wool
if 60% are cotton and 40% are wool then Total socks are 200.
60% = 120 black total - 20 wool socks = 100 black cotton
Still took me way too long though
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Re: In a shop, 40% socks are white and rest are black. 60% socks are made  [#permalink]

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New post 28 Nov 2019, 17:47
1
Bunuel wrote:
In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks are made of cotton?

(A) 100
(B) 80
(C) 60
(D) 50
(E) 25


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If the total number of socks = n, then we have:

0.4n = white and 0.6n = black

0.6n = cotton and 0.4n = wool

0.25 * 0.4n = 0.1n = white cotton, so 0.3n = white wool

Thus, 0.1n = black wool, so we have:

0.1n = 20

n = 200

So, there are 200 x 0.6 = 120 black socks and 120 - 20 = 100 are black cotton socks.

Answer: A
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Re: In a shop, 40% socks are white and rest are black. 60% socks are made  [#permalink]

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New post 28 Nov 2019, 20:05
Bunuel wrote:
In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks are made of cotton?

(A) 100
(B) 80
(C) 60
(D) 50
(E) 25


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2 by 2 MATRIX is the most suitable in such questions...

--------White--------Black--------Total
C--- --0.25*40x ----- a ---------60x ...................Thus, 0.25*40x+a=60x.....a=50x
W----------b---------20-----------40x
Total---40x-------60x------100x

So, from black socks, we get a+20=60x...50x+20=60x......10x=20....x=2
We are looking for a, which is 50x=50*2=100

A
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Re: In a shop, 40% socks are white and rest are black. 60% socks are made  [#permalink]

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New post 29 Nov 2019, 01:14
When I first looked at this question, the first thing that popped up in my brain was that there was a clear distinction between black and white, cotton and wool; this is to say that what is black cannot be white and vice versa, what is cotton cannot be wool and vice versa. This is ample evidence to say that we are dealing with a set of mutually exclusive objects. And in all such cases, we can draw up a table, fill it up and obtain our answer from it.
Since the values are given in terms of a percentage, I’d take 100 as the total number of socks. Applying the percentages given in the question and filling up the table, we get a table

Attachment:
29th Nov 2019 - Reply 2 - 1.jpg
29th Nov 2019 - Reply 2 - 1.jpg [ 27.86 KiB | Viewed 236 times ]


The question says that 20 of the black socks are made of wool. But, the table shows it as 10. This means that we will have to multiply this cell, and therefore all the other cells also, by 2. When we do that, we get a table like the one below:

Attachment:
29th Nov 2019 - Reply 2 - 2.jpg
29th Nov 2019 - Reply 2 - 2.jpg [ 28.75 KiB | Viewed 234 times ]


This means that there were a total of 200 socks of which 120 are cotton socks. Of these, from the table, we see that there are 100 cotton socks which are black.
The correct answer option is A.

Hope that helps!
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Re: In a shop, 40% socks are white and rest are black. 60% socks are made   [#permalink] 29 Nov 2019, 01:14
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