Question

An antique dealer sold three items, A, B, and C, with their selling prices in the ratio 4:5:6. He suffered a loss of 10% on item A, made a profit of 50% on item B, and broke even (no profit, no loss) on item C. What was his approximate percentage gain or loss in the overall deal?

• A. Loss of 8.88%
• B. Profit of 8.88%
• C. Profit of 10.88%
• D. Loss of 10.88%

Answer 1

Answer:

B. Profit of 8.88%

Let the selling prices of items A, B, and C be:

$4x,; 5x,; 6x$

Now calculate their cost prices.

For item A, there is a 10% loss:

$\text{CP}_A=\frac{4x}{0.9}=\frac{40x}{9}$

For item B, there is a 50% profit:

$\text{CP}_B=\frac{5x}{1.5}=\frac{10x}{3}$

For item C, there is no profit or loss:

$\text{CP}_C=6x$

Total selling price:

$4x+5x+6x=15x$

Total cost price:

$\frac{40x}{9}+\frac{10x}{3}+6x$

Taking LCM (9):

$=\frac{40x+30x+54x}{9}$
$=\frac{124x}{9}$

Now compare total SP and CP:

$15x=\frac{135x}{9}$

Profit:

$\frac{135x-124x}{9}=\frac{11x}{9}$

Profit percentage:

$\frac{\frac{11x}{9}}{\frac{124x}{9}}\times100$

$\frac{11}{124}\times100$

$\approx 8.88\%$

Therefore, the dealer made an overall profit of approximately (8.88%).