Question

A trader sells 20 articles at Rs. 54 per article after giving 10% discount and gains 50% profit. If the discount is not given, the profit gained is ______

• A. 56.76%
• B. 66.66%
• C. 62.66%
• D. 63.66%

Hint:

Find the cost price from the 50% profit, then find the marked price from the 10% discount.

Answer 1

The Correct Option is B

Step 1: Express everything as a multiple of the cost price.
Let the cost price of all 20 articles be $100k$ for some unit $k$. Since the trader gains 50% profit after the discount, the actual revenue collected is $150k$.

Step 2: Relate the revenue to the marked price.
This revenue of $150k$ is what remains after a 10% discount on the marked price $M$, so $0.9M = 150k$, which gives $M = \dfrac{150k}{0.9} = 166.67k$ (repeating).

Step 3: Work out the profit without any discount.
If no discount is given, the trader collects the full marked price $166.67k$ as revenue, while the cost price is still $100k$. Profit percentage $= \dfrac{166.67k - 100k}{100k} \times 100 = 66.67\%$.

Final Answer:
Working entirely in ratios of the cost price gives the same 66.66% profit (the small rounding is from the repeating decimal $\frac{2}{3}$). \[ \boxed{66.66\%} \]