After selling 5% of a quantity of sugar, 5 kg. of sugar remains. Find the total quantity of sugar.

Options

A. 19 kg
B. `5 5/19` kg
C. 100 kg
D. 95 kg

Answer

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

### Step 1: Define the total quantity of sugar
Let the total quantity of sugar be represented by \( x \) kg.

### Step 2: Understand the remaining quantity after selling
According to the problem, after selling 5% of the total quantity of sugar, 5 kg remains. This means that 95% of the total quantity is left.

### Step 3: Set up the equation
Since 95% of the total quantity \( x \) is equal to 5 kg, we can write the equation:
\[ 0.95x = 5 \]

### Step 4: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{5}{0.95} \]

### Step 5: Calculate \( x \)
Now, calculate \( x \):
\[ x = \frac{5 \times 100}{95} = \frac{500}{95} \]

### Step 6: Simplify the fraction
To simplify \( \frac{500}{95} \):
\[ x = \frac{500 \div 5}{95 \div 5} = \frac{100}{19} \]

### Step 7: Convert to a mixed number
Now, divide 100 by 19 to convert it into a mixed number:
\[ 100 \div 19 = 5 \quad \text{(with a remainder of 5)} \]
So, we can express it as:
\[ x = 5 \frac{5}{19} \]

### Final Answer
Thus, the total quantity of sugar is \( \frac{100}{19} \) kg or approximately \( 5.26 \) kg.