Answer :
To find the value of x, the weight of the fifth person, the sum of the given weights plus x, divided by 5 (the total number of persons), should equal the arithmetic mean of 61 kg. After setting up the equation, x is found to be 45 kg.
To find the value of x in the given problem, one must recognize that the sum of weights of all persons divided by the number of persons will give the arithmetic mean of their weights. Since the arithmetic mean is provided as 61 kg for 5 persons, we can set up an equation to solve for x.
We are given the following weights of 4 persons: 67 kg, 65 kg, 71 kg, and 57 kg. Adding these together gives us 260 kg. Let's denote the total sum of weights of all 5 persons as S. Thus, S = 260 kg + x. To find the arithmetic mean, we divide S by 5 and set it equal to 61 kg:
S/5 = 61 kg
260 + x = 61*5
260 + x = 305
x = 305 - 260
x = 45
Therefore, the weight of the fifth person is 45 kg.
