A toy train is marked at Rs. 400 and sold at a discount of 8% during Ganesh puja. A shopkeeper announces a discount of 8%. The amount he will loss if he announces a single discount of 16% is

Options

A. Rs. 2.56
B. Rs. 3.84
C. Rs. 4.16
D. Rs. 5.78

Answer

To solve the problem step by step, we need to calculate the selling price of the toy train after applying both discounts and then find the loss incurred by the shopkeeper if he had announced a single discount of 16%.

### Step 1: Calculate the selling price after the first discount of 8%.

- **Marked Price (MP)** = Rs. 400
- **Discount** = 8%

**Selling Price (SP1)** after the first discount can be calculated as:
\[ SP1 = MP - (MP \times \frac{Discount}{100}) \]
\[ SP1 = 400 - (400 \times \frac{8}{100}) = 400 - 32 = Rs. 368 \]

### Step 2: Calculate the selling price after the second discount of 8%.

The second discount of 8% is applied on the already discounted price (SP1).

**Selling Price (SP2)** after the second discount can be calculated as:
\[ SP2 = SP1 - (SP1 \times \frac{Discount}{100}) \]
\[ SP2 = 368 - (368 \times \frac{8}{100}) = 368 - 29.44 = Rs. 338.56 \]

### Step 3: Calculate the selling price if a single discount of 16% is applied.

Now, we calculate the selling price if a single discount of 16% is applied directly on the marked price.

**Selling Price (SP3)** with a single discount of 16%:
\[ SP3 = MP - (MP \times \frac{Discount}{100}) \]
\[ SP3 = 400 - (400 \times \frac{16}{100}) = 400 - 64 = Rs. 336 \]

### Step 4: Calculate the loss incurred by the shopkeeper.

Now, we find the loss by comparing SP2 and SP3:
\[ Loss = SP2 - SP3 \]
\[ Loss = 338.56 - 336 = Rs. 2.56 \]

### Final Answer:
The amount the shopkeeper will lose if he announces a single discount of 16% is **Rs. 2.56**.

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