Rani bought vegetables weighing `10` kg. Out of this, `3` kg `500` g is onions and `2` kg `75` g is potatoes and the rest is tomatoes. What is the weight of tomatoes?

Options

A. `4.429` kg
B. `4.416` kg
C. `4.425` kg
D. `4.424` kg

Answer

To find the weight of tomatoes that Rani bought, we will follow these steps:

### Step 1: Understand the total weight of vegetables
The total weight of vegetables Rani bought is given as:
\[ \text{Total weight} = 10 \text{ kg} \]

### Step 2: Convert the weights of onions and potatoes into kilograms
The weight of onions is:
\[ \text{Weight of onions} = 3 \text{ kg} + 500 \text{ g} \]
Since \( 500 \text{ g} = 0.5 \text{ kg} \), we can write:
\[ \text{Weight of onions} = 3 \text{ kg} + 0.5 \text{ kg} = 3.5 \text{ kg} \]

The weight of potatoes is:
\[ \text{Weight of potatoes} = 2 \text{ kg} + 75 \text{ g} \]
Since \( 75 \text{ g} = 0.075 \text{ kg} \), we can write:
\[ \text{Weight of potatoes} = 2 \text{ kg} + 0.075 \text{ kg} = 2.075 \text{ kg} \]

### Step 3: Calculate the total weight of onions and potatoes
Now we will add the weights of onions and potatoes:
\[ \text{Total weight of onions and potatoes} = 3.5 \text{ kg} + 2.075 \text{ kg} \]
Calculating this gives:
\[ \text{Total weight of onions and potatoes} = 5.575 \text{ kg} \]

### Step 4: Calculate the weight of tomatoes
To find the weight of tomatoes, we subtract the total weight of onions and potatoes from the total weight of vegetables:
\[ \text{Weight of tomatoes} = \text{Total weight} - \text{Total weight of onions and potatoes} \]
Substituting the values we have:
\[ \text{Weight of tomatoes} = 10 \text{ kg} - 5.575 \text{ kg} \]
Calculating this gives:
\[ \text{Weight of tomatoes} = 4.425 \text{ kg} \]

### Step 5: Convert the weight of tomatoes to kg and g
To express \( 4.425 \text{ kg} \) in kilograms and grams:
- The whole number part is \( 4 \text{ kg} \).
- The decimal part \( 0.425 \text{ kg} \) can be converted to grams by multiplying by \( 1000 \):
\[ 0.425 \text{ kg} = 0.425 \times 1000 \text{ g} = 425 \text{ g} \]

Thus, the weight of tomatoes is:
\[ \text{Weight of tomatoes} = 4 \text{ kg} \, 425 \text{ g} \]

### Final Answer
The weight of tomatoes is **4 kg 425 g**.

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