The per cent profit made when an article is sold for ₹ 56 is thrice as when it is sold for ₹ 42. The cost price of the article is :

Options

A. ₹ 48
B. ₹ 49
C. ₹ 50
D. ₹ 35

Answer

To solve the problem step by step, we need to establish the relationship between the selling prices, cost price, and profit. Let's denote the cost price of the article as \( CP \) and the profit when sold at different prices as \( x \).

### Step 1: Define the profit when sold at different prices
1. When the article is sold for ₹56, the profit is \( x \).
- Therefore, the selling price (SP) can be expressed as:
\[ SP_1 = CP + x = 56 \]
- Rearranging gives:
\[ CP = 56 - x \quad (1) \]

2. When the article is sold for ₹42, the profit is \( \frac{x}{3} \) (since the profit at ₹56 is three times that at ₹42).
- Therefore, the selling price can be expressed as:
\[ SP_2 = CP + \frac{x}{3} = 42 \]
- Rearranging gives:
\[ CP = 42 - \frac{x}{3} \quad (2) \]

### Step 2: Set the two expressions for CP equal to each other
From equations (1) and (2), we can set them equal to each other:
\[ 56 - x = 42 - \frac{x}{3} \]

### Step 3: Solve for x
1. To eliminate the fraction, multiply the entire equation by 3:
\[ 3(56 - x) = 3(42 - \frac{x}{3}) \]
This simplifies to:
\[ 168 - 3x = 126 - x \]

2. Now, rearranging gives:
\[ 168 - 126 = 3x - x \]
\[ 42 = 2x \]
\[ x = 21 \]

### Step 4: Substitute x back to find CP
Now that we have \( x = 21 \), we can substitute it back into either equation (1) or (2) to find the cost price \( CP \).

Using equation (1):
\[ CP = 56 - x = 56 - 21 = 35 \]

### Final Answer
The cost price of the article is ₹35.

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