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?

First, we identify the group size. The family groups consist of 2 children and 1 parent, so the count is 3 people. \n\nWe can solve this intuitively using the 'Difference Method' seen in 2016 PYQs [11, 59].\n1. The average weight with the Mother is 50 kg.\n2. The average weight with the Father is 52 kg.\n3. The average increased by 2 kg (52 - 50).\n\nSince this increase is distributed over 3 people, the Total Weight difference must be: \nDifference = Change in Average × Number of People \nDifference = 2 kg × 3 = 6 kg.\n\nThis means the Father is 6 kg heavier than the Mother. \nWe know the Father weighs 60 kg.\nSo, Mother's weight = 60 kg - 6 kg = 54 kg.\n\n(Alternative Check using 'Sum = Average × Count' [7]):\nTotal weight (Children + Mother) = 50 × 3 = 150 kg.\nTotal weight (Children + Father) = 52 × 3 = 156 kg.\nDifference is 6 kg. Since Father is 60, Children are 96. Then Mother is 150 - 96 = 54 kg. Both methods give the same result.