20% of product bought by a shopkeeper is damaged and are sold at 30% discount. Remaining products is sold at a discount of 10%. If difference between total selling price of products sold at 30% discounts and 10% discount is 29,000, Then find the sum of marked price of all product? (in rs)

Options

A. A)`50,000`
B. B)`40,000`
C. C)`25,000`
D. D)`75,000`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Problem
The shopkeeper has a certain number of products, 20% of which are damaged and sold at a 30% discount. The remaining 80% are sold at a 10% discount. We need to find the total marked price of all products based on the difference in selling prices.

### Step 2: Define Variables
Let the total number of products be represented as \( x \).

- Damaged products = 20% of \( x \) = \( 0.2x \)
- Undamaged products = 80% of \( x \) = \( 0.8x \)

### Step 3: Selling Price Calculation
Assume the marked price of each product is \( M \).

- Selling price of damaged products (30% discount):
\[ \text{Selling Price (SP) of damaged products} = M \times (1 - 0.3) \times (0.2x) = 0.7M \times (0.2x) = 0.14Mx \]

- Selling price of undamaged products (10% discount):
\[ \text{Selling Price (SP) of undamaged products} = M \times (1 - 0.1) \times (0.8x) = 0.9M \times (0.8x) = 0.72Mx \]

### Step 4: Difference in Selling Prices
According to the problem, the difference between the total selling price of products sold at a 30% discount and those sold at a 10% discount is 29,000:
\[ \text{Difference} = \text{SP of damaged} - \text{SP of undamaged} \]
\[ 0.72Mx - 0.14Mx = 29000 \]
\[ 0.58Mx = 29000 \]

### Step 5: Solve for \( Mx \)
Now, we can solve for \( Mx \):
\[ Mx = \frac{29000}{0.58} = 50000 \]

### Step 6: Total Marked Price Calculation
The total marked price of all products is:
\[ \text{Total Marked Price} = M \times x \]
From our calculation, \( Mx = 50000 \).

### Final Answer
Thus, the sum of the marked price of all products is:
\[ \text{Total Marked Price} = 50000 \text{ Rs} \]