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

To solve this problem, we need to find the profit percentage the trader would realize if the discount was not given. Let's break down the problem step-by-step: 

1. \(SP\) (Selling Price with Discount) = Rs. 54 per article. 
   Discount given = 10%. 
   Original Price (Marked Price, \(MP\)):

We know, \(\text{Selling Price after discount} = MP \times (1 - \frac{\text{Discount \%}}{100})\)

1. \(54 = MP \times (1 - \frac{10}{100})\) 
   \(54 = MP \times 0.9\) 
   \(MP = \frac{54}{0.9} = 60\) 
   So, Marked Price per article = Rs. 60.
2. Find the Cost Price (CP): 
   Given, Selling Price with discount gives 50% profit: 
   \(\text{Profit \%} = \frac{\text{SP - CP}}{\text{CP}} \times 100\) 
   Since profit is 50%, \(\text{ SP } = 1.5 \times \text{CP}\). 
   \(54 = 1.5 \times \text{CP}\) 
   \(\text{CP} = \frac{54}{1.5} = 36\) 
   Therefore, the Cost Price per article = Rs. 36.
3. Calculate Profit without discount: 
   If no discount is given, the selling price would be the marked price = Rs. 60. 
   Profit = SP - CP = 60 - 36 = Rs. 24.
4. Calculate Profit Percentage without Discount: 
   \(\text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100\) 
   \(\text{Profit \%} = \frac{24}{36} \times 100 = 66.66\%\)

Therefore, the profit gained if no discount is given is 66.66%.

Answer 2

Step 1: Find the total revenue and the cost price.
The trader sells 20 articles at Rs. 54 each, so total revenue \(= 20 \times 54 = \text{Rs. } 1080\). This revenue already includes a 50% profit, so cost price \(= \dfrac{1080}{1.5} = \text{Rs. } 720\).

Step 2: Find the marked price before the discount.
The revenue of Rs. 1080 was collected after a 10% discount on the marked price \(K\), so \(0.9K = 1080\), giving \(K = \dfrac{1080}{0.9} = \text{Rs. } 1200\).

Step 3: Find the profit if no discount was given.
Without a discount, the trader would collect the full marked price of Rs. 1200 as revenue while the cost price stays Rs. 720. Profit percentage \(= \dfrac{1200 - 720}{720} \times 100\).

Step 4: Simplify the fraction.
\(\dfrac{480}{720} \times 100 = 66.66\%\) (repeating).

Final Answer:
The profit without the discount would be 66.66%. \[ \boxed{66.66\%} \]