The average weight of five persons sitting in a boat is 38 kg. The average weight of the boat and the persons sitting in the boat is 52kg. What is the weight of the boat?

Options

A. 228 kg
B. 122 kg
C. 232 kg
D. 242 kg

Answer

To find the weight of the boat, we can follow these steps:

### Step 1: Calculate the total weight of the five persons.
The average weight of the five persons is given as 38 kg. To find the total weight, we use the formula for average:

\[ \text{Total Weight of Persons} = \text{Average Weight} \times \text{Number of Persons} \]

Substituting the values:

\[ \text{Total Weight of Persons} = 38 \, \text{kg} \times 5 = 190 \, \text{kg} \]

### Step 2: Calculate the total weight of the boat and the five persons.
The average weight of the boat and the five persons is given as 52 kg. The total number of entities (boat + 5 persons) is 6. We can find the total weight using the same average formula:

\[ \text{Total Weight (Boat + Persons)} = \text{Average Weight} \times \text{Total Number of Entities} \]

Substituting the values:

\[ \text{Total Weight (Boat + Persons)} = 52 \, \text{kg} \times 6 = 312 \, \text{kg} \]

### Step 3: Calculate the weight of the boat.
Now that we have the total weight of the persons and the total weight of the boat plus the persons, we can find the weight of the boat by subtracting the total weight of the persons from the total weight of the boat and persons:

\[ \text{Weight of the Boat} = \text{Total Weight (Boat + Persons)} - \text{Total Weight of Persons} \]

Substituting the values:

\[ \text{Weight of the Boat} = 312 \, \text{kg} - 190 \, \text{kg} = 122 \, \text{kg} \]

### Conclusion:
The weight of the boat is **122 kg**.

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