Mohan sold an article for RS.56 which coste him RS.x. He finds that he has gained x% on his outlay. Find x.

Answer

To solve the problem step by step, we will use the information provided to set up an equation and find the value of \( x \).

### Step 1: Understand the given information
Mohan sold an article for Rs. 56, and the cost price (CP) of the article is Rs. \( x \). He gained \( x\% \) on his outlay (cost price).

### Step 2: Set up the equation for selling price (SP)
The selling price (SP) can be expressed in terms of the cost price (CP) and profit. The formula is:
\[ \text{SP} = \text{CP} + \text{Profit} \]
The profit can be calculated as:
\[ \text{Profit} = \frac{x}{100} \times \text{CP} = \frac{x}{100} \times x = \frac{x^2}{100} \]
Thus, we can write:
\[ \text{SP} = x + \frac{x^2}{100} \]

### Step 3: Substitute the selling price
We know that the selling price is Rs. 56, so we can set up the equation:
\[ 56 = x + \frac{x^2}{100} \]

### Step 4: Eliminate the fraction
To eliminate the fraction, multiply the entire equation by 100:
\[ 5600 = 100x + x^2 \]

### Step 5: Rearrange the equation
Rearranging gives us a standard quadratic equation:
\[ x^2 + 100x - 5600 = 0 \]

### Step 6: Factor the quadratic equation
Now we need to factor the quadratic equation. We look for two numbers that multiply to \(-5600\) and add to \(100\). The numbers are \(140\) and \(-40\):
\[ (x + 140)(x - 40) = 0 \]

### Step 7: Solve for \( x \)
Setting each factor to zero gives us:
1. \( x + 140 = 0 \) → \( x = -140 \) (not possible since cost price cannot be negative)
2. \( x - 40 = 0 \) → \( x = 40 \)

Thus, the cost price \( x \) is Rs. 40.

### Final Answer
The value of \( x \) is \( 40 \).

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