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A milliner bought a job lot of hats 1/4 of which were brown.
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Updated on: 22 Nov 2018, 08:54
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73% (02:00) correct 27% (02:39) wrong based on 112 sessions
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A milliner bought a job lot of hats 1/4 of which were brown. The milliner sold 2/3 of the hats including 4/5 of the brown hats. What fraction of the unsold hats were brown? (A) 1/60 (B) 2/15 (C) 3/20 (D) 3/5 (E) 3/4 Project PS Butler : Question #34 Subscribe to get Daily Email  Click Here  Subscribe via RSS  RSS
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Originally posted by nick_sun on 22 Mar 2007, 00:43.
Last edited by HKD1710 on 22 Nov 2018, 08:54, edited 2 times in total.
Added the OA.



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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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22 Mar 2007, 01:36
Suppose he bought n hats, n/4 brown and 3n/4 not brown.
He sold 2n/3 of the hats in total ,(4/5)(n/4)=n/5 of which were brown
Remaining, then, are n/4n/5=n/20 brown hats of a total of n/3 unsold hats.
Thus the fraction of the unsold hats that are brown is n/20 divided by n/3 =3/20
C
Alternatively, suppose there are 60 hats bought (LCM(3,4,5)). 20 were unsold, and of the 15 brown hats, 3 were unsold



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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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14 Aug 2011, 02:27
i went a more difficult way to solve it,
if x = the total number of hats, then x/4 are brown hats and 3x/4 are black hats
if you sell 2/3 of the hats, and since you don't know how many of those are black or brown luckily they give you the statement that 4/5 of the brown hats were sold off in that
so 2/3x = (x/4)*(4x/5) + Y(3x/4)
I let Y be the fraction of Black hats sold, and as you can see, I included the 3x/4 which is the amount of black hats originally.
2/3*x  1/5*x = Y(3x/4) 7x/15 = Y(3x/4)
you end up with Y = 28/60 or 14/30, or in other words, the amount of black hats sold from the original 3/4.
but earlier we also figured out that 1/5*x is the amount of brown hats sold from the original 1/4. So i guess the tricky part is realizing you need to find out what is remaining after being sold. that would equal the original amount  the sold amount.
1/4*x  1/5*x = the remaining brown hats = 1/20*x 3/4*x  14/30*x = the remaining black hats = 45/60*x  28/60*x = 17/60*x
the question asks for the ratio of remaining brown to total, so divide remaining brown / total
(1/20*x) / (1/20*x + 17/60*x) x(3/60 + 17/60) = 1/20*x / (x*20/60)
= 1/20 * 60/20 = 1/20 * 3 = 3/20



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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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21 Aug 2011, 07:39
just suppose that you have a total of 60 hats. no. of brow hats = 1/4*60 = 15 of these hats, 4/5*15 = 12 were sold, so remaining brown hats = 3 no. of hats sold = 2/3*60 = 40 unsold hats = 20 ANS = 3/20
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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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21 Aug 2011, 07:51
We know 1/4 of the hats are brown acc. to given conditions 4/5th of brown hats are sold so 1/5 are unsold i.e. 1/5*(no. of brown hats are unsold) Let total no. of hats be H no.of brown hats remaining=1/4*(total no. of hats)=1/4H acc. to given conditions, 1/3 hats remain hence no. of hats remaining=1/3H there required fraction=(1/20*H)/(1/3*H)=3/20 3/20
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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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21 Aug 2011, 17:51
let T be the total and B be the brown ones.
(1/4)T = B
(2/3)T were sold, of which (4/5)T were brown. left over brown hats(unsold brown hats) = (1/4)T  (4/5)T = T/20
(1/3)T were unsold.
the fraction of unsold hats that were brown = (T/20)/ ((1/3)T) = 3/20



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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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24 Jun 2018, 09:46
Lets solve it by picking a smart number, say the milliner bought total 60 hats: Attachment:
20180624_230950.jpg [ 50.26 KiB  Viewed 1446 times ]
Correct answer is option C
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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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09 Feb 2019, 07:05
nick_sun wrote: A milliner bought a job lot of hats 1/4 of which were brown. The milliner sold 2/3 of the hats including 4/5 of the brown hats. What fraction of the unsold hats were brown?
(A) 1/60 (B) 2/15 (C) 3/20 (D) 3/5 (E) 3/4
BrownNot Brown Sold122840 Unsold31720154560 3/20
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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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18 Feb 2019, 18:05
I started this out by finding the LCM of the 3, 4, and 5, which is 60.
So let's say 60 total hats.
1/4 of them were brown = 15 brown hats.
He sold 2/3 of the hats, which would be 40 total, but 4/5 brown hats were sold off along with the 40, so 4/5 of 15 is 12 brown hats gone.
Left remaining are 20 hats, with 3 of them being brown.
3/20




Re: A milliner bought a job lot of hats 1/4 of which were brown.
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18 Feb 2019, 18:05






