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?
42 kg
Solving the Weight Relationship Problem
The problem gives us a set of relationships between the total weights of different groups of people and asks us to find the average weight of boys, given the average weight of women.
Understanding the Given Information
We are given the following equivalences based on total weight:
- Total weight of 6 boys = Total weight of 7 girls
- Total weight of 7 girls = Total weight of 3 men
- Total weight of 3 men = Total weight of 4 women
This means the total weight of 6 boys is equal to the total weight of 4 women. We can write this relationship as:
Total weight of 6 boys = Total weight of 4 women
We are also given the average weight of the women:
- Average weight of 1 woman = 63 kg
Calculating the Total Weight of Women
Since the average weight of one woman is 63 kg, the total weight of 4 women can be calculated by multiplying the average weight by the number of women.
Total weight of 4 women = Average weight per woman \(\times\) Number of women
Total weight of 4 women = \(63 \text{ kg/woman} \times 4 \text{ women}\)
Total weight of 4 women = \(252 \text{ kg}\)
Using the Relationship to Find the Total Weight of Boys
We know that the total weight of 6 boys is equal to the total weight of 4 women. We just calculated the total weight of 4 women as 252 kg.
Total weight of 6 boys = Total weight of 4 women
Total weight of 6 boys = \(252 \text{ kg}\)
Calculating the Average Weight of Boys
Now that we have the total weight of 6 boys, we can find the average weight of one boy by dividing the total weight by the number of boys.
Average weight of 1 boy = \(\frac{\text{Total weight of 6 boys}}{\text{Number of boys}}\)
Average weight of 1 boy = \(\frac{252 \text{ kg}}{6}\)
Performing the division:
\(\frac{252}{6} = 42\)
So, the average weight of one boy is 42 kg.
Summary of Calculations
| Item | Value | Calculation/Relation |
|---|---|---|
| Average weight of 1 woman | 63 kg | Given |
| Total weight of 4 women | 252 kg | \(63 \text{ kg/woman} \times 4 \text{ women}\) |
| Total weight of 6 boys | 252 kg | Equal to total weight of 4 women |
| Average weight of 1 boy | 42 kg | \(\frac{252 \text{ kg}}{6 \text{ boys}}\) |
Therefore, the average weight of the boys is 42 kg.
Revision Table: Key Concepts for Weight Problems
| Concept | Definition/Formula | Application in Problem |
|---|---|---|
| Average | \(\frac{\text{Sum of values}}{\text{Number of values}}\) | Used to find average weight from total weight and vice versa. |
| Total Weight | Average weight \(\times\) Number of individuals | Calculated for women and then inferred for boys. |
| Weight Relationship | Equivalence between total weights of different groups. | Given as \(6B = 7G = 3M = 4W\), used to link women's total weight to boys' total weight (\(6B = 4W\)). |
Additional Information: Understanding Proportional Relationships
This problem relies on understanding proportional relationships. The statement "Weight of 6 boys = Weight of 4 women" means that the total mass of 6 boys is the same as the total mass of 4 women. While the number of individuals is different, their combined weight is equal.
If we know the total weight of one group, we can find the total weight of another group if there's a direct relationship given, as in this problem. Once the total weight of a group is known, the average weight per individual in that group can be easily calculated by dividing the total weight by the number of individuals in that group.
These types of problems are common in quantitative aptitude and test the ability to translate word problems into mathematical equations and solve them step-by-step.
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