Consider the following:

Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women

If the average weight of the women is 63 kg, then what is the average weight of the boys?

The correct option is 42 kg.

Let us break down the solution step-by-step to understand why this is the correct answer.

Step 1: Understand the given relationships
We are given the relationship between the total weights of different groups:
Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women

Let $B$ be the average weight of a boy and $W$ be the average weight of a woman. Then, the total weight of 6 boys is $6B$ and the total weight of 4 women is $4W$.

From the given relationship, we can equate the total weight of the boys directly to the total weight of the women:
$6B=4W$

Step 2: Substitute the known values
We are given that the average weight of the women ($W$) is 63 kg.
Substituting $W=63$ into our equation:
$6B=4\times 63$

Step 3: Solve for the average weight of the boys ($B$)
Calculate the total weight of the 4 women:

Now, set up the equation to find $B$:
$6B=252$
Divide both sides by 6:
$B=\frac{252}{6}$
$B=42\text{kg}$

Thus, the average weight of the boys is 42 kg.