Selling price of three articel are same first sold @ 20% profit and second is sold @ 10% loss and third is sold 25% loss if is whole transtion he incur Rs.60 loss . Find the CP of the Article which was sold @ 20% profit.

Options

A. a)180
B. b)300
C. c)240
D. d)288

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the Selling Price
Let the selling price (SP) of each of the three articles be denoted as \( SP \).

### Step 2: Calculate the Selling Prices in Terms of Cost Price (CP)
1. **First Article**: Sold at 20% profit.
\[ SP = CP_1 + 0.2 \times CP_1 = 1.2 \times CP_1 \]

2. **Second Article**: Sold at 10% loss.
\[ SP = CP_2 - 0.1 \times CP_2 = 0.9 \times CP_2 \]

3. **Third Article**: Sold at 25% loss.
\[ SP = CP_3 - 0.25 \times CP_3 = 0.75 \times CP_3 \]

### Step 3: Set the Selling Prices Equal
Since all three articles have the same selling price:
\[ 1.2 \times CP_1 = 0.9 \times CP_2 = 0.75 \times CP_3 \]

### Step 4: Express CPs in Terms of a Common Variable
Let’s assume \( SP = x \). Then we can express the cost prices in terms of \( x \):
1. From the first article:
\[ CP_1 = \frac{x}{1.2} \]

2. From the second article:
\[ CP_2 = \frac{x}{0.9} \]

3. From the third article:
\[ CP_3 = \frac{x}{0.75} \]

### Step 5: Calculate Total Cost Price
The total cost price (CP) of all three articles is:
\[ CP_{total} = CP_1 + CP_2 + CP_3 \]
Substituting the values we found:
\[ CP_{total} = \frac{x}{1.2} + \frac{x}{0.9} + \frac{x}{0.75} \]

### Step 6: Find a Common Denominator
The least common multiple of the denominators (1.2, 0.9, 0.75) is 3. Thus, we can express each term:
1. \( \frac{x}{1.2} = \frac{5x}{6} \)
2. \( \frac{x}{0.9} = \frac{10x}{9} \)
3. \( \frac{x}{0.75} = \frac{4x}{3} \)

Converting to a common denominator of 18:
- \( CP_1 = \frac{15x}{18} \)
- \( CP_2 = \frac{20x}{18} \)
- \( CP_3 = \frac{24x}{18} \)

Thus,
\[ CP_{total} = \frac{15x + 20x + 24x}{18} = \frac{59x}{18} \]

### Step 7: Calculate the Loss
The total loss incurred is Rs. 60. The loss can be calculated as:
\[ CP_{total} - SP_{total} = 60 \]
Where \( SP_{total} = 3x \) (since there are three articles). Therefore:
\[ \frac{59x}{18} - 3x = 60 \]

### Step 8: Solve for x
Converting \( 3x \) into a fraction with a denominator of 18:
\[ \frac{59x}{18} - \frac{54x}{18} = 60 \]
This simplifies to:
\[ \frac{5x}{18} = 60 \]
Multiplying both sides by 18:
\[ 5x = 1080 \]
Dividing by 5:
\[ x = 216 \]

### Step 9: Find the Cost Price of the First Article
Now, substituting \( x \) back to find \( CP_1 \):
\[ CP_1 = \frac{x}{1.2} = \frac{216}{1.2} = 180 \]

### Final Answer
The cost price of the article which was sold at 20% profit is Rs. 180.

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