Question

Gill sold two dogs at the same price. In one, he gets a profit of 22% and in the other, he gets a loss of 22%. What is Gill's profit or loss percentage?

• A. 4.4% profit
• B. 4.84% loss
• C. 4.84% profit
• D. 4.4% loss

Answer 1

Answer:

B. 4.84% loss

Let selling price of each dog = (S)

Dog 1 (22% profit):

$CP_1 = \frac{S}{1.22}$

Dog 2 (22% loss):

$CP_2 = \frac{S}{0.78}$

Total CP:

$CP = \frac{S}{1.22} + \frac{S}{0.78}$

LCM idea:
$1.22 = \frac{122}{100}, \quad 0.78 = \frac{78}{100}$
So:
$CP = \frac{100S}{122} + \frac{100S}{78}$

LCM of 122 and 78 = 4758

$CP = \frac{100S \cdot 39 + 100S \cdot 61}{4758}$

$= \frac{3900S + 6100S}{4758}$
$= \frac{10000S}{4758}$
$CP = \frac{5000S}{2379}$

Total SP:
2S

Profit/Loss:

Compare CP and SP:

CP > SP \Rightarrow \text{loss}

Loss percentage:
$\frac{CP - SP}{CP} \times 100$

$= \frac{\frac{10000S}{4758} - 2S}{\frac{10000S}{4758}} \times 100$
$= \frac{10000 - 9516}{10000} \times 100$
$= \frac{484}{10000} \times 100$
$= 4.84\%$

Final Answer: 4.84% loss