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

Question

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

KarishmaB · Accepted Answer

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)

CounterSniper · Answer

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

manishasingh · Answer

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

ScottTargetTestPrep · Answer

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

vatsal323 · Answer

The question asks for the value of a and not the value of a%. So shouldn't the answer be 1/11 and not 100/11? I know 1/11 is not there in the options here. But asking for clarity's sake

beeblebrox · Answer

Hi  VeritasKarishma ,

The explanation is really cool, but my question is the CP could have been 11.5 or 10.9. You just picked up an integer 11.

While this approach helps in solving the question quickly, but is this the right approach in the first place?

Thanks.

KarishmaB · Answer

Note that profit and loss percents are same i.e. "a%".
They are calculated on cost price as the base. 
If the selling prices are 10 and 12, the ONLY POSSIBLE value of CP is 11 to give you the same profit % and loss %. 
Try to put CP = 11.5 and you will find that profit % will be less than loss %.
Try to put CP =10.9 and you will find that profit % is greater than loss %.

Now think, if selling prices were 10 and 15, what would be the CP?

shiva90 · Answer

Taking X as Cost price of 12 Candies

a is profit/Loss %

we get X(1-a/100)=10.......(I) -Loss eq
&
X(1+a/100)=12.........(II)-Profit eq
Solving above two eqs-
we get
 a=100/11

option-C

CrackverbalGMAT · Answer

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?

Since profit % and loss % are the same , we can conclude that loss and the profit amount is the same.

Profit = a % of CP and loss = a % of CP

Loss in the first case = Profit in the second case

CP - 10 = 12 - CP

2 CP = 22
CP = 11

Inorder to find a , Lets consider Case 1, SP = 10 and CP = 11.
Loss % = a % =  \frac{1}{11}  * 100 = 100/11

Option C is the answer.

Thanks,
 Clifin J Francis,
GMAT SME

DIPTO420 · Answer

cp = 12y ( y = per candy cp)

loss, 12y-10 = 12y*x%..............(1)
profit ,12-12y=12y*x%

12y-10 =12-12y
24y=22
y=11/12

From (1)

1=11*x%
1/11 =x%
100/11 = x

bumpbot · Answer

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

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