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

Correct Answer: 50 kg

Step-by-Step Explanation:

Step 1: Calculate the total weight of all 9 persons.
We are given that the average weight of 9 persons is 50 kg.
The formula for the total sum of items given the average is:
Total Weight = Average Weight × Number of Persons

$\text{Total weight of 9 persons}=9\times 50=450\text{kg}$

Step 2: Calculate the total weight of the first 5 persons.
The average weight of the first 5 persons is 45 kg.

$\text{Total weight of first 5 persons}=5\times 45=225\text{kg}$

Step 3: Calculate the total weight of the last 5 persons.
The average weight of the last 5 persons is 55 kg.

$\text{Total weight of last 5 persons}=5\times 55=275\text{kg}$

Step 4: Find the weight of the 5th person.
Notice that when we add the weight of the first 5 persons and the last 5 persons, the 5th person is included in both groups (i.e., counted twice).
Therefore:

$\text{Sum of (first 5 + last 5 persons)}=225+275=500\text{kg}$

To find the weight of the 5th person, we subtract the total weight of all 9 persons from this combined sum:

$\text{Weight of 5th person}=500-450=50\text{kg}$

Thus, the weight of the 5th person is 50 kg.