Correct Option (D)
Let C₁ and C₂ represent the weights of the two children, M the weight of the mother, and F the weight of the father.
- The average weight of the children and their mother is 50 kg.
(C₁ + C₂ + M) / 3 = 50 kg
The total weight of the children and mother is: C₁ + C₂ + M = 50 × 3 = 150 kg (Equation 1)
- The average weight of the children and their father is 52 kg.
(C₁ + C₂ + F) / 3 = 52 kg
The total weight of the children and father is: C₁ + C₂ + F = 52 × 3 = 156 kg (Equation 2)
- The weight of the father (F) is given as 60 kg.
- Substitute the father's weight into Equation 2 to find the combined weight of the children:
C₁ + C₂ + 60 = 156
C₁ + C₂ = 156 - 60
C₁ + C₂ = 96 kg
- Now, substitute the combined weight of the children (C₁ + C₂ = 96 kg) into Equation 1 to find the mother's weight:
96 + M = 150
M = 150 - 96
M = 54 kg
Therefore, the weight of the mother is 54 kg.
Incorrect Options:
Options A (48 kg), B (50 kg), and C (52 kg) are incorrect. These values for the mother's weight would not satisfy the conditions established by the given average weights of the family members when subjected to the calculations derived from the problem statement.