Make a video explaining the answer to this ques.---**Question Number:** 50.
**Question Stem (English):**
A dealer offers a cash discount of 20% and still makes a profit of 20%, if he further sell 8 articles at a rate of 6 articles. Then how much percentage above the cost price does he mark on each article?
**Question Stem (Hindi):**
एक विक्रेता 20% की नकद छूट (डिस्काउंट) देता है और फिर भी 20% का लाभ प्राप्त करता है। यदि वह 8 वस्तुओं को 6 वस्तुओं के मूल्य पर बेचता है। तो वह प्रत्येक वस्तु पर क्रय मूल्य से कितना प्रतिशत अधिक मूल्य अंकित करता है?
**Options:**
a) 77.5%
b) 100%
c) 112.5%
d) 87.5%
**Chart/Diagram Description:**
The image contains a handwritten diagram illustrating the relationship between Cost Price (CP), Selling Price (SP), and Marked Price (MP).
* Three labeled circles are present: "CP", "SP", and "MP".
* An arrow goes from CP to SP, labeled with an expression involving fractions and a multiplication sign (partially visible). The visible part seems to be related to profit.
* An arrow goes from MP to SP, labeled with an expression "x 4/5". This likely represents a 20% discount (1 - 20/100 = 80/100 = 4/5).
* An arrow goes from CP to MP, indicated by a curved line.
* Handwritten calculations are present below the diagram:
* A fraction 6/5 is crossed out.
* A multiplication expression is shown: 6/5 * 8/6 * 5/4 =.
* Some numbers are crossed out within the multiplication (6, 5, 6, 5, 4).
* Simplified numbers are written above the crossed out numbers: 2 above 8, 2 above 4 (partially visible, looks like 2/2 = 1).
* The result of the calculation is partially visible, showing "= ".
**Other Relevant Text:**
* Footer text: "Maths with Bhutesh sir", "e1", "1".
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Let's solve this step by step. We have a dealer who gives a 20% discount but still makes 20% profit. Additionally, he sells 8 articles at the price of only 6 articles. We need to find his markup percentage above cost price.
First, let's establish the key relationships. When a 20% discount is given, the selling price becomes 80% of the marked price. This means SP equals MP times 4/5. Therefore, the ratio of marked price to selling price is 5 to 4.
Now let's analyze the profit condition. The dealer sells 8 articles but receives payment for only 6 articles. With a 20% profit, the total revenue equals 1.2 times the total cost. This gives us the equation: 6 times SP equals 8 times CP times 1.2. Solving this, we get SP over CP equals 8 over 5.
Now we can find the markup ratio by combining our two ratios. MP over CP equals MP over SP times SP over CP. This gives us 5 over 4 times 8 over 5. Multiplying the numerators: 5 times 8 equals 40. Multiplying the denominators: 4 times 5 equals 20. So MP over CP equals 40 over 20, which simplifies to 2.
Finally, let's calculate the markup percentage. Since MP equals 2 times CP, the markup amount is MP minus CP, which equals CP. The markup percentage is the markup amount divided by cost price, times 100%. This gives us CP over CP times 100%, which equals 100%. Therefore, the answer is option b: 100%.