A family has two children along with their parents. The average of the weights of the children and their mother is 50 kg. The average of the weights of the children and their father is 52 kg. If the weight of the father is 60 kg, then what is the weight of the mother?

The correct option is 54 kg.

Let the weights of the two children be represented by $C_1$ and $C_2$, the weight of the mother by $M$, and the weight of the father by $F$.

Step 1: Use the average weight of the children and their mother to write an equation.
The average weight of the two children and their mother is given as 50 kg. Since there are 3 individuals (two children and one mother), we can express this as:
$\frac{C_1+C_2+M}{3}=50$

Multiplying both sides by 3, we get the sum of their weights:
$C_1+C_2+M=150$ (Equation 1)

Step 2: Use the average weight of the children and their father to write a second equation.
The average weight of the two children and their father is given as 52 kg. Similarly, we write:
$\frac{C_1+C_2+F}{3}=52$

Multiplying both sides by 3, we find the sum of their weights:
$C_1+C_2+F=156$ (Equation 2)

Step 3: Subtract Equation 1 from Equation 2 to find the relationship between the father's weight and the mother's weight.
$(C_1+C_2+F)-(C_1+C_2+M)=156-150$
This simplifies directly to:
$F-M=6$

Step 4: Substitute the father's weight into the equation to calculate the mother's weight.
We are given that the weight of the father ($F$) is 60 kg. Substituting this value:
$60-M=6$
Rearranging the equation to solve for $M$:
$M=60-6$
$M=54$

Thus, the weight of the mother is 54 kg.