A shopkeeper sells an article for Rs 78 and earns double the profit that he would have earned on selling this article for Rs 69. Find the C.P of this article.

Options

A. 60
B. 55.5
C. 61.5
D. 62

Answer

To find the cost price (C.P) of the article, we can follow these steps:

### Step 1: Define the variables
Let the cost price (C.P) of the article be Rs. X.

### Step 2: Calculate the profit at different selling prices
1. When the article is sold for Rs. 69, the profit can be expressed as:
\[ \text{Profit at Rs. 69} = 69 - X \]

2. When the article is sold for Rs. 78, the profit is:
\[ \text{Profit at Rs. 78} = 78 - X \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the profit earned when selling at Rs. 78 is double the profit earned when selling at Rs. 69. Therefore, we can write the equation:
\[ 78 - X = 2(69 - X) \]

### Step 4: Simplify the equation
Expanding the right side of the equation gives:
\[ 78 - X = 138 - 2X \]

### Step 5: Rearrange the equation
To isolate X, we can add 2X to both sides and subtract 78 from both sides:
\[ 78 - X + 2X = 138 - 78 \]
This simplifies to:
\[ X = 138 - 78 \]

### Step 6: Calculate the value of X
Now, calculate the right side:
\[ X = 60 \]

### Conclusion
Thus, the cost price (C.P) of the article is Rs. 60.