A certain manufacturer sells a product to the distributor at 10% profit. Then the distributor sells it to the dealer and the dealer sells to the retailer at a mark up of 10% and 20% respectively. The retailer marks up his cost by 20% and then offers a 10% discount to the customer. If the customer had bought it from the distributor directly at the distributor’s selling price, then how much reduction in price would he have got with respect to buying it from the retailer?

Options

A. `29.6%`
B. `18%`
C. `32%`
D. `22.8%`

Answer

To solve the problem step by step, we will calculate the selling prices at each stage of the distribution chain and then find the reduction in price when buying directly from the distributor compared to buying from the retailer.

### Step 1: Calculate the Manufacturer's Selling Price to Distributor
Let's assume the cost price (CP) for the manufacturer is ₹100.

- Profit for the manufacturer = 10% of CP
- Selling Price (SP) for the distributor = CP + Profit
- SP = ₹100 + (10% of ₹100) = ₹100 + ₹10 = ₹110

**Hint:** Start with the manufacturer's cost price and apply the profit percentage to find the selling price.

### Step 2: Calculate the Distributor's Selling Price to Dealer
The distributor sells the product to the dealer at a 10% profit.

- Profit for the distributor = 10% of ₹110
- SP for the dealer = ₹110 + (10% of ₹110) = ₹110 + ₹11 = ₹121

**Hint:** Use the selling price from the previous step as the cost price for the distributor and apply the profit percentage.

### Step 3: Calculate the Dealer's Selling Price to Retailer
The dealer sells the product to the retailer at a 20% profit.

- Profit for the dealer = 20% of ₹121
- SP for the retailer = ₹121 + (20% of ₹121) = ₹121 + ₹24.2 = ₹145.2

**Hint:** Again, use the dealer's selling price as the cost price for the dealer and apply the profit percentage.

### Step 4: Calculate the Retailer's Selling Price to Customer
The retailer marks up his cost by 20% and then offers a 10% discount.

- Markup by retailer = 20% of ₹145.2
- SP before discount = ₹145.2 + (20% of ₹145.2) = ₹145.2 + ₹29.04 = ₹174.24

Now, apply the discount of 10% on this selling price.

- Discount = 10% of ₹174.24 = ₹17.424
- Final Selling Price (SP) for the customer = ₹174.24 - ₹17.424 = ₹156.816 (approximately ₹156.82)

**Hint:** Calculate the markup on the retailer's cost price first, then apply the discount to find the final price to the customer.

### Step 5: Calculate the Reduction in Price
Now, we compare the price if the customer bought directly from the distributor.

- Distributor's Selling Price = ₹121

Now, we find the reduction in price:

- Reduction = Retailer's SP - Distributor's SP
- Reduction = ₹156.82 - ₹121 = ₹35.82

**Hint:** Subtract the distributor's selling price from the retailer's selling price to find the reduction.

### Final Answer
The customer would have saved ₹35.82 if he had bought the product directly from the distributor instead of from the retailer.