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A decorator bought a bolt of defective cloth that he judged to be 3/4

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A decorator bought a bolt of defective cloth that he judged to be 3/4  [#permalink]

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New post 13 Jun 2017, 10:02
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Difficulty:

  55% (hard)

Question Stats:

67% (02:17) correct 33% (01:59) wrong based on 72 sessions

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A decorator bought a bolt of defective cloth that he judged to be 3/4 usable, in which case the cost would be $0.80 per usable yard. If it was later found that only 2/3 of the bolt could be used, what was the actual cost per usable yard?

A. $0.60
B. $0.90
C. $1.00
D. $1.20
E. $1.70

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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4  [#permalink]

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New post 13 Jun 2017, 10:12
1
Assume the bolt of defective cloth to be 300 yards.
Since the decorator bought assuming it to be 3/4th usable,
225 yards was usable as per the decorator
Cost of the cloth was 225*0.8$ = 180$

Since afterwards, only 2/3rd was considered useful, 200 yards*x = 180$
where x was the actual cost incurred per usable yard

Actual cost of the cloth (x) = 180/200 = 0.9$ (Option B)
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4  [#permalink]

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New post 13 Jun 2017, 10:23
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Let the total unit length of cloth be 12 yards.

As per decorator's judgment, usable part = 3/4 * 12 = 9 yards.
Cost of decorator actually, in total = $ 0.8*9 = $ 7.2

In reality, usable part = 2/3 * 12 = 8 yards.
So actual cost per usable yard = 7.2/8 = $ 0.9

Hence B answer

(Please note that this answer is not affected by the length that we assume, be it 12 yards or 300 yards - we just have to take care of fractions while calculating)
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4  [#permalink]

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New post 13 Jun 2017, 10:34
Bunuel wrote:
A decorator bought a bolt of defective cloth that he judged to be 3/4 usable, in which case the cost would be $0.80 per usable yard. If it was later found that only 2/3 of the bolt could be used, what was the actual cost per usable yard?

A. $0.60
B. $0.90
C. $1.00
D. $1.20
E. $1.70



Let total amount of fabric = T
Hence total useable amount he judged = ¾ T
$0.8/Useable yard x Total Useable amount = Total paid by decorator = $0.6 T

He later found out that only ⅔ T was actually useable and he already paid $0.6T, so what changes here to maintain the total he already pad ($0.6T) is the amount paid per useable yard.

Let actual cost per useable yard = y
Hence actual total useable amount = ⅔ T
$y/Useable yard x Total Useable Amount = $0.6 T ----> y * ⅔ T = 0.6 T -----> y = $0.9/Useable yard
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4  [#permalink]

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New post 15 Jun 2017, 11:11
Let's assume - he bought 100 yards ,
3/4 usable means - 75 yards was usable
total cost - cost/usable yard * usable yards (0.8*75) = 60

Actual usable is 66.7 yards

cost/usable yard = total cost/usable yard (60/66.7) = 0.8989 or 0.9
Answer IMO B
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A decorator bought a bolt of defective cloth that he judged to be 3/4  [#permalink]

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New post 01 Dec 2018, 01:46
Total number of yards 60

1 yard = 8 EUR

\(\frac{3}{4}*60\) = \(45\) yards

total cost of 45 usable yards = 45 *8 = 360 EUR

Later turned out \(\frac{2}{3}*60 = 40\) to be usable

In this case price would be \(\frac{360}{40}= 90\) per yard

B :)
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A decorator bought a bolt of defective cloth that he judged to be 3/4 &nbs [#permalink] 01 Dec 2018, 01:46
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