On the marked price of a article ,the difference between the two selling prices ,one with a single discount of 45 % and the other with two successive discounts of 20 % and 25 % ,is Rs. 124 .What is the marked price (in Rs. )of the article ?

Options

A. 2540
B. 2480
C. 2520
D. 2500

Answer

Let's solve the problem step by step.

### Step 1: Define the Marked Price
Let the marked price of the article be denoted as \( M \).

### Step 2: Calculate Selling Price with Single Discount
The selling price (SP) after a single discount of 45% can be calculated as:
\[ SP_1 = M - (45\% \text{ of } M) = M - 0.45M = 0.55M \]

### Step 3: Calculate Selling Price with Successive Discounts
To find the selling price with two successive discounts of 20% and 25%, we first apply the 20% discount:
\[ \text{After 20% discount: } SP_2 = M - (20\% \text{ of } M) = M - 0.20M = 0.80M \]
Now, we apply the 25% discount on the new price:
\[ SP_2 = 0.80M - (25\% \text{ of } 0.80M) = 0.80M - 0.20M = 0.60M \]

### Step 4: Set Up the Equation
According to the problem, the difference between the two selling prices is Rs. 124:
\[ SP_1 - SP_2 = 124 \]
Substituting the expressions we found:
\[ 0.55M - 0.60M = 124 \]
This simplifies to:
\[ -0.05M = 124 \]

### Step 5: Solve for Marked Price
Now, we can solve for \( M \):
\[ M = \frac{124}{-0.05} = -2480 \]
Since the marked price cannot be negative, we take the absolute value:
\[ M = 2480 \]

### Conclusion
The marked price of the article is Rs. 2480.

---