Question

Average weight of five persons is 51 kg and each of them in different weights. If the average weight of heaviest and lightest persons is 52 kg and the average weight of second heaviest and fourth heaviest persons is 48 kg, then find the weight of the third lightest person?

• A. 63 kg
• B. 48 kg
• C. 32 kg
• D. 55 kg

Answer 1

The Correct Option is D

The average weight of five persons is given as 51 kg. This allows us to determine the total weight of these five persons. Let's denote the weights of these five persons as \( a, b, c, d, e \) with the condition \( a < b < c < d < e \). The total weight equation can be expressed as:

\[ \frac{a + b + c + d + e}{5} = 51 \] 

\[ a + b + c + d + e = 255 \]

We also have that the average weight of the heaviest and lightest (i.e., \( a \) and \( e \)) is 52 kg:

\[ \frac{a + e}{2} = 52 \]

\[ a + e = 104 \]

Moreover, the average weight of the second heaviest and fourth heaviest persons (i.e., \( b \) and \( d \)) is 48 kg:

\[ \frac{b + d}{2} = 48 \]

\[ b + d = 96 \]

Substituting \( a + e \) and \( b + d \) into the total weight equation gives:

\[ a + e + b + d + c = 255 \]

Substituting \( a + e = 104 \) and \( b + d = 96 \):

\[ 104 + 96 + c = 255 \]

\[ 200 + c = 255 \]

\[ c = 55 \]

Therefore, the weight of the third lightest person is 55 kg.