The average weight of 6 persons decreases by 2.5 kg when a new person comes in place of one of them weighing 70 kg. What is the weight (in kg) of the new person?

Options

A. 60
B. 75.5
C. 62.5
D. 55

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We know that the average weight of 6 persons decreases by 2.5 kg when a new person replaces one of them who weighs 70 kg. We need to find the weight of the new person.

### Step 2: Let the average weight of the 6 persons be \( x \)
Let the average weight of the 6 persons before the new person arrives be \( x \) kg.

### Step 3: Calculate the total weight of the 6 persons
The total weight of the 6 persons can be calculated as:
\[ \text{Total weight} = \text{Average weight} \times \text{Number of persons} = 6x \]

### Step 4: Calculate the new average weight
When the new person replaces the one weighing 70 kg, the average weight decreases by 2.5 kg. Therefore, the new average weight becomes:
\[ x - 2.5 \text{ kg} \]

### Step 5: Calculate the new total weight
The total weight after the new person replaces the 70 kg person is:
\[ \text{New total weight} = \text{New average weight} \times \text{Number of persons} = 6(x - 2.5) \]

### Step 6: Set up the equation
The new total weight can also be expressed as the old total weight minus the weight of the person who left (70 kg) plus the weight of the new person (let's denote it as \( y \)):
\[ \text{New total weight} = 6x - 70 + y \]

### Step 7: Equate the two expressions for the new total weight
Now we can set the two expressions for the new total weight equal to each other:
\[ 6(x - 2.5) = 6x - 70 + y \]

### Step 8: Simplify the equation
Expanding the left side gives:
\[ 6x - 15 = 6x - 70 + y \]

### Step 9: Solve for \( y \)
Now, we can simplify the equation:
\[ -15 = -70 + y \]
Adding 70 to both sides gives:
\[ y = 70 - 15 \]
\[ y = 55 \]

### Conclusion
The weight of the new person is \( 55 \) kg.

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