Marked price of an article is Rs. 800 is sold at two equal successive discounts of x% equivalent to a single discount of Rs. 350 then what will be the value of x?

Options

A. 15
B. 20
C. 25
D. 33.33

Answer

To find the value of \( x \) in the given problem, we can follow these steps:

### Step 1: Understand the Problem
We have a marked price (MP) of an article which is Rs. 800. The article is sold at two equal successive discounts of \( x\% \). The total discount is equivalent to a single discount of Rs. 350.

### Step 2: Calculate the Selling Price (SP)
The selling price (SP) after a total discount of Rs. 350 can be calculated as:
\[ SP = MP - \text{Total Discount} \]
Substituting the values:
\[ SP = 800 - 350 = 450 \]

### Step 3: Set Up the Equation for Successive Discounts
When two successive discounts of \( x\% \) are applied, the selling price can also be expressed as:
\[ SP = MP \times (1 - \frac{x}{100}) \times (1 - \frac{x}{100}) \]
This simplifies to:
\[ SP = 800 \times \left(1 - \frac{x}{100}\right)^2 \]

### Step 4: Equate the Two Expressions for SP
Now we can set the two expressions for SP equal to each other:
\[ 450 = 800 \times \left(1 - \frac{x}{100}\right)^2 \]

### Step 5: Solve for \( x \)
First, divide both sides by 800:
\[ \frac{450}{800} = \left(1 - \frac{x}{100}\right)^2 \]
This simplifies to:
\[ \frac{9}{16} = \left(1 - \frac{x}{100}\right)^2 \]

Next, take the square root of both sides:
\[ \sqrt{\frac{9}{16}} = 1 - \frac{x}{100} \]
This gives us:
\[ \frac{3}{4} = 1 - \frac{x}{100} \]

Now, rearranging the equation:
\[ \frac{x}{100} = 1 - \frac{3}{4} = \frac{1}{4} \]
Thus, multiplying both sides by 100:
\[ x = 25 \]

### Conclusion
The value of \( x \) is \( 25\% \).