Profit and Loss

[shankar.ashwin]

If a man sold 12 chocolates for $10, he would yield a loss of a%, had he sold the 12 chocolates for $12 he would have gained a% profit. What is the value of 'a'?

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

[neelgandham]

If a man sold 12 chocolates for $10, he would yield a loss of 10%, had he sold the 12 chocolates for $12 he would have gained a% profit. What is the value of 'a'?

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

Loss % = (10-X)/X = -10/100 => X = 100/9
Profit % = (12-X)/X = a/100 => (12-(100/9))/(100/9) = 8/100 => a = 8 ?

Where did I go wrong ?? :banghead:

[shankar.ashwin]

Hey sorry, typo... try now. loss in a% not 10

Loss % = (10-X)/X = -10/100 => X = 100/9
Profit % = (12-X)/X = a/100 => (12-(100/9))/(100/9) = 8/100 => a = 8 ?

Where did I go wrong ?? :banghead:

[neelgandham]

No problemos Senor !

Let X be the cost price of 12 Chocolat, then

(x-10)/x = (12-x)/x = a/100
Implies (x-10)=(12-x) => x =11

(12-x)/x = a/100 => (12-11)/11 = a/100 => a = 100/11

IMO:C

[user123321]

from given,

10(1+a/100) = 12(1-a/100)
=>22a/100 = 2
=>a = 100/11

user123321

[GMATGuruNY]

If a man sold 12 chocolates for $10, he would yield a loss of a%, had he sold the 12 chocolates for $12 he would have gained a% profit. What is the value of 'a'?

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

The distance between the cost and the lower selling price = a% of the cost.
The distance between the cost and the higher selling price = a% of the cost.
Since each selling price is the SAME DISTANCE from the cost, the cost must be HALFWAY BETWEEN the two selling prices:
Cost = $11.

The selling prices are integers.
ALWAYS LOOK AT THE ANSWER CHOICES before you do any math.

Since answer choices A and B are FRACTIONAL percentages, neither will yield integer values for the two selling prices. Eliminate A and B.
Neither D (10% of 11) nor E (11% of 11) will yield integer values for the two selling prices. Eliminate D and E.

The correct answer is C.

Answer choice C: 100/11 percent = 100/1100 = 1/11.
Loss/profit = (1/11)*11 = 1.
Lower selling price = 11-1 = 10.
Higher selling price = 11+1 = 12.
Success!

For those who favor a more direct approach, given a cost of $11, we can quickly calculate the change in percentage from 11 to 12:
(12-11)/11 * 100 = 100/11.