Selling price of an article becomes Rs2160 after giving two successive discounts of x% and 25% and marked price of article is Rs.3600. Find the cost price of article if there is a profit of x% on selling the article after giving two successive discounts.

Options

A. A)Rs 1720
B. B)Rs 1500
C. C)Rs 1600
D. D)Rs 1800

Answer

To solve the problem step by step, we will follow the logical sequence based on the information given in the question.

### Step 1: Understand the Problem
We are given:
- Marked Price (MP) = Rs 3600
- Selling Price (SP) after two successive discounts = Rs 2160
- The first discount is x% and the second discount is 25%.
- There is a profit of x% on the cost price (CP).

### Step 2: Set Up the Equation for Selling Price
The selling price after two successive discounts can be expressed as:
\[ SP = MP \times \left(1 - \frac{x}{100}\right) \times \left(1 - \frac{25}{100}\right) \]

Substituting the values we have:
\[ 2160 = 3600 \times \left(1 - \frac{x}{100}\right) \times \left(1 - 0.25\right) \]

### Step 3: Simplify the Equation
The second discount of 25% can be expressed as:
\[ 1 - 0.25 = \frac{3}{4} \]

So, the equation becomes:
\[ 2160 = 3600 \times \left(1 - \frac{x}{100}\right) \times \frac{3}{4} \]

### Step 4: Solve for x
Now, we can rearrange the equation:
\[ 2160 = 3600 \times \frac{3}{4} \times \left(1 - \frac{x}{100}\right) \]

Calculating \( 3600 \times \frac{3}{4} \):
\[ 3600 \times \frac{3}{4} = 2700 \]

So, we have:
\[ 2160 = 2700 \times \left(1 - \frac{x}{100}\right) \]

Dividing both sides by 2700:
\[ \frac{2160}{2700} = 1 - \frac{x}{100} \]

Calculating \( \frac{2160}{2700} \):
\[ \frac{2160}{2700} = \frac{24}{30} = \frac{4}{5} = 0.8 \]

Thus, we have:
\[ 0.8 = 1 - \frac{x}{100} \]

Rearranging gives:
\[ \frac{x}{100} = 1 - 0.8 = 0.2 \]

So,
\[ x = 0.2 \times 100 = 20 \]

### Step 5: Find the Cost Price
Now that we have \( x = 20\% \), we can find the cost price (CP). The selling price is given by:
\[ SP = CP \times \left(1 + \frac{x}{100}\right) \]
Substituting the values:
\[ 2160 = CP \times \left(1 + \frac{20}{100}\right) \]
\[ 2160 = CP \times 1.2 \]

Now, solving for CP:
\[ CP = \frac{2160}{1.2} \]

Calculating \( \frac{2160}{1.2} \):
\[ CP = 1800 \]

### Final Answer
The cost price of the article is Rs 1800.

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