The cost price of an article is Rs214. After allowing three successive discount of 15%, 20% and 10% on its list price, it is sold for Rs 153. If it is sold at the list price , profit , (in Rs) will be :

Options

A. 49
B. 36
C. 39
D. 45

Answer

To solve the problem step by step, we need to find the list price of the article and then calculate the profit when it is sold at that price.

### Step 1: Define the List Price
Let the list price of the article be \( X \).

### Step 2: Calculate the Selling Price After Discounts
The article is sold after applying three successive discounts of 15%, 20%, and 10%.

- After a 15% discount, the selling price becomes:
\[ X \times \left(1 - \frac{15}{100}\right) = X \times \frac{85}{100} = 0.85X \]

- After a 20% discount on the new price (0.85X), the selling price becomes:
\[ 0.85X \times \left(1 - \frac{20}{100}\right) = 0.85X \times \frac{80}{100} = 0.68X \]

- After a 10% discount on the new price (0.68X), the selling price becomes:
\[ 0.68X \times \left(1 - \frac{10}{100}\right) = 0.68X \times \frac{90}{100} = 0.612X \]

### Step 3: Set Up the Equation
According to the problem, the selling price after all discounts is Rs. 153. Therefore, we can set up the equation:
\[ 0.612X = 153 \]

### Step 4: Solve for X
To find \( X \), we rearrange the equation:
\[ X = \frac{153}{0.612} \]
Calculating this gives:
\[ X \approx 250 \]

### Step 5: Calculate Profit
Now that we have the list price \( X = 250 \) and the cost price is given as Rs. 214, we can calculate the profit:
\[ \text{Profit} = \text{List Price} - \text{Cost Price} = 250 - 214 = 36 \]

### Final Answer
The profit when sold at the list price is Rs. 36.

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