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?

Correct Answer: (D) 54 kg

Let the total weight of the two children be $C$. Given $\frac{C+M}{3}=50⟹C+M=150$$\frac{C + M}{3}$ = 50 $\implies$ C + M = 150, and $\frac{C+F}{3}=52⟹C+F=156$$\frac{C + F}{3}$ = 52 $\implies$ C + F = 156. Subtracting gives $F - M = 6$$\text{ kg}$. With father's weight $F = 60$$\text{ kg}$, mother's weight is $M = 60 - 6 = 54$$\text{ kg}$.