In a certain election, several students collected signatures to place a candidate on the ballot . Of these signatures . 25 percent wer thrown out as invalid . Then a further 20 percent of those remaining were eliminated. What percent of the original number of signatures were left ?

Options

A. `40%`
B. `45%`
C. `55%`
D. `60%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Total Number of Signatures
Let the total number of original signatures be \( x \).

### Step 2: Calculate the Remaining Signatures After Invalid Signatures
According to the problem, 25% of the signatures were thrown out as invalid. Therefore, the percentage of signatures that remain is:
\[ 100\% - 25\% = 75\% \]
So, the number of remaining signatures after this step is:
\[ 0.75x \]

### Step 3: Calculate the Remaining Signatures After Further Elimination
Next, 20% of the remaining signatures are eliminated. This means that 80% of the remaining signatures are still valid. Therefore, the number of remaining signatures after this elimination is:
\[ 80\% \text{ of } 0.75x = 0.80 \times 0.75x \]
Calculating this gives:
\[ 0.80 \times 0.75 = 0.60 \]
So, the number of remaining signatures is:
\[ 0.60x \]

### Step 4: Calculate the Percentage of Original Signatures Remaining
Now, we need to find out what percentage of the original number of signatures \( x \) is represented by the remaining signatures \( 0.60x \). The formula for percentage is:
\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]
In this case, the part is \( 0.60x \) and the whole is \( x \):
\[ \text{Percentage} = \left( \frac{0.60x}{x} \right) \times 100 \]
Since \( x \) cancels out, we have:
\[ \text{Percentage} = 0.60 \times 100 = 60\% \]

### Final Answer
Thus, the percentage of the original number of signatures that were left is:
\[ \boxed{60\%} \]