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Selling 12 candies at a price of $10 yields a loss of a%. Selling 12

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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
GPA: 3.68
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New post 11 Sep 2018, 01:40
3
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

56% (02:33) correct 44% (02:36) wrong based on 52 sessions

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Selling 12 candies at a price of $10 yields a loss of a%. Selling 12 candies at a price of $12 yields a profit of a%. What is the value of a?

A)11/1100
B)11/100
C)100/11
D)10
E)11
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Selling 12 candies at a price of $10 yields a loss of a%. Selling 12  [#permalink]

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New post 11 Sep 2018, 01:48
2
2
selim wrote:
Selling 12 candies at a price of $10 yields a loss of a%. Selling 12 candies at a price of $12 yields a profit of a%. What is the value of a?

A)11/1100
B)11/100
C)100/11
D)10
E)11


loss percent = profit percent = a
a= \(\frac{(cp-10)}{cp}\)*100 = \(\frac{(12-cp)}{cp}\) *100
=> cp-10 = 12-cp => cp =11

a= \(\frac{(11-10)*100}{11}\)=\(\frac{100}{11}\)
C
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Joined: 31 May 2018
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Selling 12 candies at a price of $10 yields a loss of a%. Selling 12  [#permalink]

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New post 11 Apr 2019, 01:57
Let C be cost of each candy
Cost of 12 candies is 12C

Selling 12 candies at $10 yields a loss of a%

We know, Loss % = \(\frac{CP-SP}{CP}\) * 100

Hence, a% = \(\frac{12C-10}{12C}\) * 100 ---- Eq. 1

Selling 12 candies at $12 yields a profit of a%

We know, Profit% = \(\frac{SP-CP}{CP}\) * 100

Hence, a% =\(\frac{12-12C}{12C}\) * 100 --- Eq. 2

Equating Eq. 1 & 2, we have:

\(\frac{12-12C}{12C}\) * 100 = \(\frac{12C-10}{12C}\) *100

12-12C = 12C - 10

24C = 22

C = \(\frac{22}{24}\) = \(\frac{11}{12}\)

From Eq. 1 we have,

a% = \(\frac{12C-10}{12C}\)

a% =\(\frac{12*11}{12}\)-10/ \(\frac{11}{12}\)* 12

a% = \(\frac{11-10}{11}\)

a% = \(\frac{1}{11}\)

a = \(\frac{100}{11}\)

Option C- correct ans
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Re: Selling 12 candies at a price of $10 yields a loss of a%. Selling 12  [#permalink]

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New post 11 Apr 2019, 02:55
2
KSBGC wrote:
Selling 12 candies at a price of $10 yields a loss of a%. Selling 12 candies at a price of $12 yields a profit of a%. What is the value of a?

A)11/1100
B)11/100
C)100/11
D)10
E)11


If SP = 10, loss is a%
If SP = 12, profit is a%

So CP must be right in between 10 and 12 to get the same loss and profit.
CP = 11

Profit of a% = (12-11)/11 * 100 = 100/11%

Answer (C)
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Re: Selling 12 candies at a price of $10 yields a loss of a%. Selling 12  [#permalink]

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New post 14 Apr 2019, 18:51
KSBGC wrote:
Selling 12 candies at a price of $10 yields a loss of a%. Selling 12 candies at a price of $12 yields a profit of a%. What is the value of a?

A)11/1100
B)11/100
C)100/11
D)10
E)11


Let c = the cost of the 12 candies. We can create the equations:

120 - c = -(a/100)c

120 - c = -ac/100

and

144 - c = (a/100)c

144 - c = ac/100

Adding the equations together, we have:

264 - 2c = 0

264 = 2c

132 = c

Thus:

144 - 132 = a(132)/100

12 = a(132)/100

1200 = 132a

a = 1200/132 = 300/33 = 100/11

Answer: C
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Re: Selling 12 candies at a price of $10 yields a loss of a%. Selling 12   [#permalink] 14 Apr 2019, 18:51
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