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 ✓ UPSC's answer

Why the answer is (d)

• Let the weights of the two children be $C_1$ and $C_2$, the mother be $M$, and the father be $F$.

• The average weight of the children and the mother is 50 kg, so $C_1 + C_2 + M = 3 \times 50 = 150$ kg.

• The average weight of the children and the father is 52 kg, so $C_1 + C_2 + F = 3 \times 52 = 156$ kg.

• We are given that the father's weight $F = 60$ kg.

• Substituting $F = 60$ into the second equation gives $C_1 + C_2 + 60 = 156$, which implies $C_1 + C_2 = 96$ kg.

• Substituting $C_1 + C_2 = 96$ into the first equation gives $96 + M = 150$, so $M = 150 - 96 = 54$ kg.

Why the other options are wrong

(a) 48 kg: 48 kg is incorrect because it results from an arithmetic error in subtracting the children's combined weight from the total.
(b) 50 kg: 50 kg is incorrect because it assumes the mother's weight equals the average of the group including her, ignoring the father's higher weight.
(c) 52 kg: 52 kg is incorrect because it confuses the mother's weight with the average weight of the group including the father.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.