The price of an article is first decreased by 20% and then increased by 30%. If the resulting price is 416, the original price of the article is

Options

A. ₹ 350
B. ₹405
C. ₹ 400
D. ₹ 450

Answer

Let's solve the problem step by step.

### Step 1: Define the Original Price
Let the original price of the article be \( x \).

### Step 2: Calculate the Price After the Decrease
The price is first decreased by 20%. To find the new price after this decrease, we calculate:
\[ \text{Price after decrease} = x - 0.20x = 0.80x \]

### Step 3: Calculate the Price After the Increase
Next, the price is increased by 30%. We calculate the new price after this increase:
\[ \text{Price after increase} = 0.80x + 0.30(0.80x) = 0.80x + 0.24x = 1.04x \]

### Step 4: Set Up the Equation
According to the problem, the resulting price after these changes is 416. Therefore, we can set up the equation:
\[ 1.04x = 416 \]

### Step 5: Solve for \( x \)
To find the original price \( x \), we divide both sides of the equation by 1.04:
\[ x = \frac{416}{1.04} \]
Calculating this gives:
\[ x = 400 \]

### Conclusion
The original price of the article is \( \boxed{400} \).

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