The average weight of 47 balls is 4 gm. If the weight of the bag (in which the balls are kept) be included, the calculated average weight per ball increases by 0.3 gm. What is the weight of the bag?

Options

A. 14.8 gm
B. 15.0 gm
C. 18.6 gm
D. None of these

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total weight of the balls.
The average weight of the balls is given as 4 gm, and there are 47 balls.
To find the total weight of the balls, we use the formula:

\[ \text{Total weight of balls} = \text{Average weight} \times \text{Number of balls} \]

Substituting the values:

\[ \text{Total weight of balls} = 4 \, \text{gm} \times 47 = 188 \, \text{gm} \]

### Step 2: Determine the new average weight when the bag is included.
When the weight of the bag is included, the average weight per ball increases by 0.3 gm. Therefore, the new average weight is:

\[ \text{New average weight} = 4 \, \text{gm} + 0.3 \, \text{gm} = 4.3 \, \text{gm} \]

### Step 3: Calculate the total weight including the bag.
Now, we need to find the total weight when the bag is included. The total number of items (balls + bag) is 48 (47 balls + 1 bag). We can calculate the total weight using the new average:

\[ \text{Total weight including bag} = \text{New average weight} \times \text{Total number of items} \]

Substituting the values:

\[ \text{Total weight including bag} = 4.3 \, \text{gm} \times 48 = 206.4 \, \text{gm} \]

### Step 4: Calculate the weight of the bag.
To find the weight of the bag, we subtract the total weight of the balls from the total weight including the bag:

\[ \text{Weight of the bag} = \text{Total weight including bag} - \text{Total weight of balls} \]

Substituting the values:

\[ \text{Weight of the bag} = 206.4 \, \text{gm} - 188 \, \text{gm} = 18.4 \, \text{gm} \]

### Conclusion:
The weight of the bag is **18.4 gm**.

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