20 kg of a mixture of wheat and husk contains 5% husk. How many kg more of husk must be added to make the husk content 20% in the new mixture?

Options

A. 2.75
B. 3.75
C. 4.75
D. 5.75

Answer

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

### Step 1: Determine the initial amount of husk in the mixture
The mixture weighs 20 kg and contains 5% husk.
To find the amount of husk, we calculate:
\[ \text{Amount of husk} = 5\% \text{ of } 20 \text{ kg} = \frac{5}{100} \times 20 = 1 \text{ kg} \]

### Step 2: Determine the amount of wheat in the mixture
Since the total weight of the mixture is 20 kg and we have 1 kg of husk, the amount of wheat can be calculated as:
\[ \text{Amount of wheat} = 20 \text{ kg} - 1 \text{ kg} = 19 \text{ kg} \]

### Step 3: Set up the equation for the new mixture
Let \( x \) be the amount of husk we need to add. After adding \( x \) kg of husk, the new total weight of the mixture will be:
\[ \text{New total weight} = 20 \text{ kg} + x \text{ kg} \]
The new amount of husk will be:
\[ \text{New amount of husk} = 1 \text{ kg} + x \text{ kg} \]

### Step 4: Set the equation for the new percentage of husk
We want the new mixture to have 20% husk. Therefore, we can set up the equation:
\[ \frac{1 + x}{20 + x} = 20\% \]
Converting 20% to a fraction gives us:
\[ \frac{1 + x}{20 + x} = \frac{20}{100} = \frac{1}{5} \]

### Step 5: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 5(1 + x) = 1(20 + x) \]
Expanding both sides results in:
\[ 5 + 5x = 20 + x \]

### Step 6: Rearranging the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 5x - x = 20 - 5 \]
\[ 4x = 15 \]

### Step 7: Solve for \( x \)
Dividing both sides by 4 gives:
\[ x = \frac{15}{4} = 3.75 \text{ kg} \]

### Conclusion
Thus, the amount of husk that must be added to make the husk content 20% in the new mixture is:
\[ \boxed{3.75 \text{ kg}} \]