# Tug of War Quiz Puzzle

In a Tug of War competition there have been the following results:

Two boys and three girls beat their father,

The mother beat one boy and four girls,

And the father and one boy beat the mother and three girls.

What would be the outcome if the mother and two boys took on the father and three girls?

Assume that all boys pull equally and all girls pull equally.

## 1 comment

• Shivansh Sharma

The following 3 equations are given:
2b + 3g > f -—(1)
m > b + 4g -—(2)
f + b > m + 3g -—(3)

Adding (1), (2), and (3), we get

2b + 3g + m + f + b > f + b + 4g + m + 3g
Simplifying:
3b + 3g > b + 7g
2b > 4g
or
b > 2g -—(4)

Now from eq.(1), we have
2b + 3g > f
Adding 3g to both sides, we get
2b + 6g > f + 3g
or
(b + 4g) + b + 2g > f + 3g

Replacing (b + 4g) by (m) from eq.(2). The inequality will still hold.
m + b + 2g > f + 3g

replacing (2g) by (b) from eq.(4). The inequality will still hold.
m + b + b > f + 3g
or
m + 2b > f + 3g

And that is what we needed to calculate.
The mother and two boys will beat the father and three girls.