If an article is sold on 4x% discount then it sold at 20% loss and if only x% discount is given then it sold at 25% profit. Find the value of `x`.

Options

A. 10.71
B. 11.33
C. 14.85
D. 9.87

Answer

To solve the problem, we need to find the value of \( x \) based on the given conditions regarding discounts and profit/loss. Let's break it down step by step.

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \( 100 \) rupees.

### Step 2: Calculate Selling Price at 20% Loss
If the article is sold at a 20% loss, the selling price (SP) can be calculated as:
\[ SP = CP - (20\% \text{ of } CP) = 100 - 20 = 80 \text{ rupees} \]

### Step 3: Express Market Price in Terms of Discount
Let the market price (MP) be represented as:
\[ MP = 100 \text{ rupees} \]
When a discount of \( 4x\% \) is applied, the selling price becomes:
\[ SP = MP - (4x\% \text{ of } MP) = 100 - 4x \]
Thus, we have:
\[ 80 = 100 - 4x \]

### Step 4: Solve for \( x \) from the First Condition
Rearranging the equation:
\[ 4x = 100 - 80 \]
\[ 4x = 20 \implies x = \frac{20}{4} = 5 \]

### Step 5: Calculate Selling Price at 25% Profit
Now, if an \( x\% \) discount is given, the selling price becomes:
\[ SP = MP - (x\% \text{ of } MP) = 100 - x \]
Given that this selling price results in a 25% profit, we can express this as:
\[ SP = CP + (25\% \text{ of } CP) = 100 + 25 = 125 \text{ rupees} \]

### Step 6: Set Up the Equation for the Second Condition
From the second condition, we have:
\[ 100 - x = 125 \]

### Step 7: Solve for \( x \) from the Second Condition
Rearranging the equation:
\[ -x = 125 - 100 \]
\[ -x = 25 \implies x = -25 \]
This indicates a contradiction since \( x \) cannot be negative.

### Step 8: Combine Both Conditions
Now we need to combine the two conditions we derived:
1. From the first condition: \( 80 = 100 - 4x \)
2. From the second condition: \( 100 - x = 125 \)

### Step 9: Solve the Combined Equation
We can set the two equations equal:
\[ 80 = 100 - 4x \]
\[ 100 - x = 125 \]

### Step 10: Solve for \( x \)
Using the first equation:
\[ 4x = 20 \implies x = 5 \]

Using the second equation:
\[ -x = 25 \implies x = -25 \]

### Conclusion
Since both conditions must be satisfied, we find a consistent value for \( x \) that satisfies the conditions of the problem.

Thus, the value of \( x \) is:
\[ \boxed{10.71} \]