Question 17/20: Set 2 - Try Out - Mathematical Reasoning (SNBT)

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Number 17

Two study groups have $4$ members each. Their average body weights are $30\text{ kg}$ and $33\text{ kg}$ . If one child from each group is swapped, the average body weight becomes equal. The difference in body weight between the two swapped children is...

$1\frac{1}{2}\text{ kg}$

$2\text{ kg}$

$4\text{ kg}$

$6\text{ kg}$

$8\text{ kg}$

Explanation

Initial Total Weight Analysis

First, let's calculate the total body weight of each group before the swap. Group A has $4$ members with an average of $30\text{ kg}$ . Group B has $4$ members with an average of $33\text{ kg}$ .

\text{Total A} = 4 \times 30 = 120\text{ kg}

\text{Total B} = 4 \times 33 = 132\text{ kg}

The Swap Process

Let the child leaving Group A be $x_A$ and the child leaving Group B be $x_B$ . After swapping, $x_A$ joins Group B and $x_B$ joins Group A.

For the averages of both groups to be equal after the swap (given the number of members remains the same), the total body weight of both groups must also be equal.

We can write this new balance equation as follows:

\text{New Total A} = \text{New Total B}

120 - x_A + x_B = 132 - x_B + x_A

Calculating the Difference

Our goal is to find the difference in body weight between the two swapped children, which is $|x_B - x_A|$ . We group the terms:

x_B + x_B - x_A - x_A = 132 - 120

2x_B - 2x_A = 12

2(x_B - x_A) = 12

x_B - x_A = 6

Thus, the difference in body weight between the two swapped children is $6\text{ kg}$ .

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Number 17

Explanation