The average weight of nine mangoes increases by 20 g if one of them weighing 120 g is replaced by another. The weight of the new mango is

Options

A. 180 g
B. 200 g
C. 260 g
D. 300 g

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
We know that the average weight of nine mangoes increases by 20 g when a mango weighing 120 g is replaced by another mango.

### Step 2: Calculate the initial total weight of the nine mangoes
Let the initial average weight of the nine mangoes be \( A \). The total weight of the nine mangoes can be expressed as:
\[ \text{Total initial weight} = 9A \]

### Step 3: Calculate the new average weight
Since the average weight increases by 20 g, the new average weight becomes:
\[ \text{New average weight} = A + 20 \]

### Step 4: Calculate the new total weight of the mangoes
The total weight of the nine mangoes after replacing one mango is:
\[ \text{Total new weight} = 9(A + 20) = 9A + 180 \]

### Step 5: Set up the equation for the total weight after replacement
When the mango weighing 120 g is replaced by a new mango weighing \( x \), the total weight can also be expressed as:
\[ \text{Total new weight} = \text{Total initial weight} - 120 + x = 9A - 120 + x \]

### Step 6: Equate the two expressions for the total new weight
Now we can set the two expressions for the total new weight equal to each other:
\[ 9A + 180 = 9A - 120 + x \]

### Step 7: Simplify the equation
Subtract \( 9A \) from both sides:
\[ 180 = -120 + x \]

### Step 8: Solve for \( x \)
Add 120 to both sides:
\[ x = 180 + 120 = 300 \]

### Conclusion
The weight of the new mango is \( 300 \) g.

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