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 answer is (D) 54 kg.
Explanation:
Let the weights of the two children be C1 and C2, and the weights of mother and father be M and F. Given: average weight of children and mother = 50 kg. Therefore, (C1 + C2 + M) / 3 = 50, which means C1 + C2 + M = 150. Also, average weight of children and father = 52 kg. Therefore, (C1 + C2 + F) / 3 = 52, which means C1 + C2 + F = 156. We are given the weight of the father F = 60 kg. Substituting F in the second equation: C1 + C2 + 60 = 156, which gives C1 + C2 = 96 kg. Now substitute C1 + C2 = 96 into the first equation: 96 + M = 150, which gives M = 150 - 96 = 54 kg. Let's re-verify: 96 + 54 = 150. Thus, the weight of the mother is 54 kg. Let's check options: 48 kg, 50 kg, 52 kg, 54 kg. Option index 3 corresponds to 54 kg.
हिंदी में प्रश्न एवं आदर्श उत्तर
किसी परिवार में दो बच्चे हैं और उनके माता-पिता हैं। बच्चों और उनकी माता के वज़नों का औसत 50 kg है। बच्चों और उनके पिता के वज़नों का औसत 52 kg है। यदि पिता का वज़न 60 kg है, तो माता का वज़न कितना है?
सही उत्तर (D) 54 kg है।
व्याख्या:
Let the weights of the two children be C1 and C2, and the weights of mother and father be M and F. Given: average weight of children and mother = 50 kg. Therefore, (C1 + C2 + M) / 3 = 50, which means C1 + C2 + M = 150. Also, average weight of children and father = 52 kg. Therefore, (C1 + C2 + F) / 3 = 52, which means C1 + C2 + F = 156. We are given the weight of the father F = 60 kg. Substituting F in the second equation: C1 + C2 + 60 = 156, which gives C1 + C2 = 96 kg. Now substitute C1 + C2 = 96 into the first equation: 96 + M = 150, which gives M = 150 - 96 = 54 kg. Let's re-verify: 96 + 54 = 150. Thus, the weight of the mother is 54 kg. Let's check options: 48 kg, 50 kg, 52 kg, 54 kg. Option index 3 corresponds to 54 kg.