Suresh has three boxes of different fruits. Box 1 weighs `2(1)/2` -kg more than Box 2 and Box 3 weighs `10(1)/4` kg more than Box 2. If the total weight of the three boxes is `48(3)/4` kg, find the weight of each box.

Answer

To solve the problem step by step, we will define the weights of the boxes in terms of a variable and then set up an equation based on the information provided.

### Step 1: Define the Variables
Let the weight of Box 2 be \( x \) kg.

### Step 2: Express the Weights of Box 1 and Box 3
According to the problem:
- Box 1 weighs \( 2.5 \) kg more than Box 2. Therefore, the weight of Box 1 can be expressed as:
\[ \text{Weight of Box 1} = x + 2.5 \]
- Box 3 weighs \( 10.25 \) kg more than Box 2. Therefore, the weight of Box 3 can be expressed as:
\[ \text{Weight of Box 3} = x + 10.25 \]

### Step 3: Set Up the Equation
The total weight of the three boxes is given as \( 48.75 \) kg. Therefore, we can write the equation:
\[ \text{Weight of Box 1} + \text{Weight of Box 2} + \text{Weight of Box 3} = 48.75 \]
Substituting the expressions we found:
\[ (x + 2.5) + x + (x + 10.25) = 48.75 \]

### Step 4: Simplify the Equation
Now, combine like terms:
\[ 3x + 2.5 + 10.25 = 48.75 \]
This simplifies to:
\[ 3x + 12.75 = 48.75 \]

### Step 5: Solve for \( x \)
To isolate \( x \), subtract \( 12.75 \) from both sides:
\[ 3x = 48.75 - 12.75 \]
\[ 3x = 36 \]
Now, divide by \( 3 \):
\[ x = 12 \]

### Step 6: Find the Weights of Each Box
Now that we have \( x \), we can find the weights of each box:
- Weight of Box 2:
\[ \text{Weight of Box 2} = x = 12 \text{ kg} \]
- Weight of Box 1:
\[ \text{Weight of Box 1} = x + 2.5 = 12 + 2.5 = 14.5 \text{ kg} \]
- Weight of Box 3:
\[ \text{Weight of Box 3} = x + 10.25 = 12 + 10.25 = 22.25 \text{ kg} \]

### Final Answer
The weights of the boxes are:
- Box 1: \( 14.5 \) kg
- Box 2: \( 12 \) kg
- Box 3: \( 22.25 \) kg