A group of boys has an aver age weight of 36 kg. One boy weighing 42 kg leaves the group and another boy weighing 30 kg joins the group. If the average now becomes `35.7` kg. then how many boys are there in the group?

Options

A. 30
B. 32
C. 40
D. 56

Answer

To solve the problem step by step, let's denote the number of boys in the group as \( x \).

### Step 1: Calculate the total initial weight of the boys
The average weight of the boys is given as 36 kg. Therefore, the total weight of the boys in the group can be calculated as:
\[ \text{Total initial weight} = \text{Average weight} \times \text{Number of boys} = 36 \times x \]

### Step 2: Account for the boy leaving and the boy joining
When one boy weighing 42 kg leaves the group, the total weight decreases by 42 kg. When another boy weighing 30 kg joins, the total weight increases by 30 kg. Thus, the new total weight can be calculated as:
\[ \text{New total weight} = (36x - 42 + 30) = 36x - 12 \]

### Step 3: Set up the equation for the new average weight
After the changes, the number of boys in the group becomes \( x - 1 + 1 = x \) (since one boy leaves and one boy joins). The new average weight is given as 35.7 kg. Therefore, we can set up the equation:
\[ \frac{36x - 12}{x} = 35.7 \]

### Step 4: Solve the equation for \( x \)
To eliminate the fraction, multiply both sides by \( x \):
\[ 36x - 12 = 35.7x \]

Now, rearranging the equation gives:
\[ 36x - 35.7x = 12 \]
\[ 0.3x = 12 \]

Now, divide both sides by 0.3 to find \( x \):
\[ x = \frac{12}{0.3} = 40 \]

### Conclusion
Thus, the number of boys in the group is \( \boxed{40} \).

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