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Set Algebra

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Junior | Next Rank: 30 Posts
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by alishagmat » Fri Oct 02, 2020 4:14 am

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Answers

A

B

C

D

E

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Difficulty—

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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Re: Set Algebra

by deloitte247 » Thu Oct 08, 2020 9:14 am
Given that white socks = 40%
Cotton socks = 60%
White socks with cotton = 25% of white socks
Black socks with wool =20
Let total no. of socks = x
White socks = 0.4x
Black socks = x - 0.4x = 0.6x
Cotton socks = 0.6x wool socks = x - 0.6x = 0.4x
White socks with cotton = 25% of white socks = 25% of 0.4x = 0.1x
White socks with wool = total white socks - white socks with cotton
= 0.4x - 0.1x = 0.3x
Black socks with wool = 20
Total socks with wool = white socks with wool + black socks with wool
0.4x = 0.3x + 20
0.4x - 0.3x = 20
0.1x = 20
x = 20/0.1 = 200
Total black socks = black socks with cotten + black socks with wool
Black socks with cotten = total black socks - black socks with wool
= 0.6x - 20 where x = 200
= 0.6(200) - 20
= 120 - 20
= 100
Answer = option A
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