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

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Bunuel
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A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   13 Jun 2017, 11:02
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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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B
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amanvermagmat
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   13 Jun 2017, 11:23
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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] New post   13 Jun 2017, 11:12
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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] New post   13 Jun 2017, 11:34
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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] New post   15 Jun 2017, 12:11
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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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   01 Dec 2018, 02:46
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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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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   07 Apr 2019, 08:37
Tricky as hell :(
got it wrong
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   18 Sep 2019, 08:15
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


inverse proportion: \(x=k/y…k=xy…k=(3/4)(4/5)…k=(2/3)(x)\)
\((3/4)(4/5)=(2/3)x…x=(12/20)(3/2)=36/40=0.9\)

Answer (B)
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   18 Sep 2019, 13:15
T - total $
x - total area/bolt/cloth

T/(3/4*x)=0.80 => T/x=0.6

T/(2/3*x)=3/2*T/x=3/2*0.6=0.9
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A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   23 Sep 2019, 09:36
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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


We can let the total length of the cloth be 60 yards, so 3/4 x 60 = 45 yards were originally thought to be usable, and the cost of the cloth would be 0.8 x 45 = $36. However, since only 2/3 x 60 = 40 yards are actually usable, the cost per yard is 36/40 = $0.90.

Answer: B
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   05 Sep 2020, 18:49
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?

Let total cloth be C
Usable cloth = (3/4)*C
Rate per usable yard = $0.80

Total Initial Cost = (Rate per usable yard) * (Usable Cloth) = (3/4*C) * 0.80 = 0.60C

Actual usable cloth = (2/3)*C
Actual Cost per usable yard = Total Initial Cost / Actual usable cloth = 0.60C / (2/3)*C = $0.90..............(B)
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A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   02 Jul 2022, 21:40
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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


Fabric is 1 yard.
If it were 3/4 usable, 0.75 yard usable.
0.75 * $0.80 = $0.60

If it were 2/3 usable, 0.66667 yard usable.
0.66667 * what = $0.60
$0.90

Answer choice B.
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink] New post   23 Jul 2023, 23:57
As per given fractions 3/4 and 2/3, we can assume the length of cloth be a multiple of LCM of (3,4)=12, lets assume the the length of cloth equal to 60 since we have a decimal also to work with in the given problem.

Case 1: usable =3/4 of cloth = 3*60/4=45
Total cost=45*0.8 (Given than $0.8 is cost per usable cloth)
=36

Actual case, usable = 2*60/3=40

Therefore cost per usable cloth = Total cost/Actual usable = 36/40=$0.9

Hence B
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Re: A decorator bought a bolt of defective cloth that he judged to be 3/4 [#permalink]
23 Jul 2023, 23:57
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