Question

A clothing store sold three dresses, D1, D2, and D3, whose selling prices were in the ratio 5:6:7. They made a profit of 20% on D1, a loss of 10% on D2, and a profit of 30% on D3. What was their approximate total profit or loss percentage for the entire sale?

• A. Profit of 12.25%
• B. Loss of 10.98%
• C. Profit of 10.99%
• D. loss of 12.25%

Answer 1

Answer:

C. Profit of 10.99%

Let the selling prices of the three dresses be in the ratio 5 : 6 : 7.

So, let:

• D1 SP = ₹5x

• D2 SP = ₹6x

• D3 SP = ₹7x

  Step 1: Find Cost Prices

  D1: 20% profit

$CP_1 = \frac{5x}{1.20} = \frac{25x}{6}$

D2: 10% loss

$CP_2 = \frac{6x}{0.90} = \frac{20x}{3}$

D3: 30% profit

$CP_3 = \frac{7x}{1.30} = \frac{70x}{13}$

Step 2: Total SP

$SP = 5x+6x+7x = 18x$

Step 3: Total CP

$CP = \frac{25x}{6}+\frac{20x}{3}+\frac{70x}{13}$

Using a common denominator of 78:

$CP = \frac{325x+520x+420x}{78}$
$= \frac{1265x}{78}$
$\approx 16.218x$

Step 4: Profit

$\text{Profit} = 18x - 16.218x$
= 1.782x

Step 5: Profit Percentage

$\text{Profit \%}$
$= \frac{1.782}{16.218}\times 100$
$\approx 10.99\%$