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11 Sep 2018, 01:40
3
00:00

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
Director
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management

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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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9218
Location: Pune, India

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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

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