The average weight of 25 candles is 40 gram. If some candles of weight 50 gram each were removed, then average weight becomes 37.5 gram. How many candles of weight 50 gram each were removed?

Options

A. 3
B. 5
C. 8
D. 12

Answer

To solve the problem step by step, we will use the information given in the question about the average weights of the candles before and after some were removed.

### Step 1: Calculate the total weight of the 25 candles.
The average weight of 25 candles is given as 40 grams. We can calculate the total weight of these candles using the formula:

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

\[ \text{Total Weight} = 40 \, \text{grams} \times 25 = 1000 \, \text{grams} \]

**Hint:** To find the total weight, multiply the average weight by the number of items.

### Step 2: Let \( x \) be the number of 50-gram candles removed.
We denote the number of 50-gram candles removed as \( x \). The total weight of the removed candles is:

\[ \text{Weight of Removed Candles} = 50 \, \text{grams} \times x \]

### Step 3: Calculate the new total weight after removing the candles.
After removing \( x \) candles, the new total weight of the remaining candles becomes:

\[ \text{New Total Weight} = 1000 \, \text{grams} - 50x \]

### Step 4: Calculate the number of remaining candles.
After removing \( x \) candles from the original 25, the number of remaining candles is:

\[ \text{Remaining Candles} = 25 - x \]

### Step 5: Set up the equation for the new average weight.
The new average weight of the remaining candles is given as 37.5 grams. We can set up the equation using the formula for average:

\[ \text{Average Weight} = \frac{\text{Total Weight}}{\text{Number of Candles}} \]

Substituting the values we have:

\[ 37.5 = \frac{1000 - 50x}{25 - x} \]

### Step 6: Cross-multiply to eliminate the fraction.
Cross-multiplying gives us:

\[ 37.5(25 - x) = 1000 - 50x \]

### Step 7: Distribute and simplify the equation.
Distributing \( 37.5 \):

\[ 937.5 - 37.5x = 1000 - 50x \]

### Step 8: Rearrange the equation to isolate \( x \).
Bringing all terms involving \( x \) to one side and constant terms to the other side:

\[ 50x - 37.5x = 1000 - 937.5 \]

This simplifies to:

\[ 12.5x = 62.5 \]

### Step 9: Solve for \( x \).
Dividing both sides by 12.5:

\[ x = \frac{62.5}{12.5} = 5 \]

### Conclusion:
The number of candles of weight 50 grams each that were removed is \( \boxed{5} \).

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