Suman purchased `5kg` `75g` of fruits and `3kg` `465g` of vegetables, and put them in a bag. If this bag with these contents weighs `9kg`, find the weight of the empty bag.

Options

A. `1kg` `480g`
B. `2kg` `460g`
C. `2kg` `467g`
D. `1kg` `460g`

Answer

To find the weight of the empty bag, we will follow these steps:

### Step 1: Convert the weights of fruits and vegetables into kilograms.
- **Fruits**: Suman purchased 5 kg 75 g of fruits.
- Convert 75 g to kg:
\[ 75 \text{ g} = \frac{75}{1000} \text{ kg} = 0.075 \text{ kg} \]
- Therefore, the total weight of fruits in kg is:
\[ 5 \text{ kg} + 0.075 \text{ kg} = 5.075 \text{ kg} \]

- **Vegetables**: Suman purchased 3 kg 465 g of vegetables.
- Convert 465 g to kg:
\[ 465 \text{ g} = \frac{465}{1000} \text{ kg} = 0.465 \text{ kg} \]
- Therefore, the total weight of vegetables in kg is:
\[ 3 \text{ kg} + 0.465 \text{ kg} = 3.465 \text{ kg} \]

### Step 2: Add the weights of fruits and vegetables.
- Now, we add the weight of fruits and vegetables:
\[ 5.075 \text{ kg} + 3.465 \text{ kg} = 8.540 \text{ kg} \]

### Step 3: Find the weight of the empty bag.
- We know that the total weight of the bag with its contents is 9 kg. To find the weight of the empty bag, we subtract the total weight of fruits and vegetables from the total weight:
\[ \text{Weight of the bag} = 9 \text{ kg} - 8.540 \text{ kg} = 0.460 \text{ kg} \]

### Step 4: Convert the weight of the bag to grams.
- To convert 0.460 kg to grams:
\[ 0.460 \text{ kg} = 0.460 \times 1000 \text{ g} = 460 \text{ g} \]

### Final Answer:
The weight of the empty bag is **460 grams**.

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