The average weight of a group of 5 boys is 26. If we replace a boy of weight 25 in the group with another boy so that new average increases by 3, find the weight of the new body.

Options

A. 33
B. 40
C. 34
D. 56

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Calculate the total weight of the original group of boys.
The average weight of the group of 5 boys is given as 26. To find the total weight of the boys, we can use the formula for average:

\[ \text{Total Weight} = \text{Average Weight} \times \text{Number of Boys} \]

So, the total weight of the 5 boys is:

\[ \text{Total Weight} = 26 \times 5 = 130 \]

### Step 2: Understand the change in average weight.
When one boy weighing 25 is replaced by a new boy, the average weight increases by 3. Therefore, the new average weight becomes:

\[ \text{New Average} = 26 + 3 = 29 \]

### Step 3: Set up the equation for the new total weight.
After replacing the boy weighing 25 with the new boy (let's denote the weight of the new boy as \( x \)), the total weight of the group becomes:

\[ \text{New Total Weight} = \text{Old Total Weight} - 25 + x \]

Substituting the known total weight:

\[ \text{New Total Weight} = 130 - 25 + x = 105 + x \]

### Step 4: Relate the new total weight to the new average.
Since the new average is 29 for the 5 boys, we can express this as:

\[ \text{New Total Weight} = \text{New Average} \times \text{Number of Boys} \]

Thus,

\[ 105 + x = 29 \times 5 \]

Calculating the right side:

\[ 29 \times 5 = 145 \]

So we have:

\[ 105 + x = 145 \]

### Step 5: Solve for \( x \).
To find the weight of the new boy, we solve the equation:

\[ x = 145 - 105 \]

Calculating this gives:

\[ x = 40 \]

### Conclusion:
The weight of the new boy is **40**.

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