Suppose the average weight of 9 persons is 50 kg. The average weight of the first 5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the 5th person will be

(a) 45 kg
(b) 47·5 kg
(c) 50 kg ✓ UPSC's answer
(d) 52·5 kg

Why the answer is (c)

• The total weight of all 9 persons is calculated as 9 multiplied by the average weight of 50 kg, which equals 450 kg.

• The total weight of the first 5 persons is 5 multiplied by their average weight of 45 kg, resulting in 225 kg.

• The total weight of the last 5 persons is 5 multiplied by their average weight of 55 kg, resulting in 275 kg.

• The sum of the weights of the first 5 and the last 5 persons is 225 kg + 275 kg = 500 kg.

• This sum includes the weight of the 5th person twice, as they are the common person in both groups (positions 1-5 and 5-9).

• Therefore, the weight of the 5th person is the difference between the combined sum of the two groups and the total weight of all 9 persons: 500 kg - 450 kg = 50 kg.

Why the other options are wrong

(a) 45 kg: 45 kg is the average weight of the first five persons, not the specific weight of the fifth person.
(b) 47·5 kg: 47.5 kg is the arithmetic mean of the two group averages (45 and 55), which is not the correct method to find the overlapping individual's weight.
(d) 52·5 kg: 52.5 kg is not derived from the correct calculation of the overlap between the two groups.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.