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 ?
- A.48 kg
- B.50 kg
- C.52 kg
- D.54 kg
▶ Answer & Explanation
Correct answer: D. 54 kg
Let the weights of the two children be C1 and C2, the mother's weight be M, and the father's weight be F. The average weight of children and mother is 50 kg, so (C1 + C2 + M) / 3 = 50. The average weight of children and father is 52 kg, so (C1 + C2 + F) / 3 = 52. Given F = 60 kg, we can find the sum of children's weights from the second equation: C1 + C2 + 60 = 52 * 3 = 156, which means C1 + C2 = 156 - 60 = 96 kg. Substituting this sum into the first equation: (96 + M) / 3 = 50, so 96 + M = 50 * 3 = 150. Therefore, M = 150 - 96 = 54 kg.
Source: UPSC csat 2019