The area of a square sheet is 250 sq. cm. If one-fourth of the sheet is painted red, then half of the sheet is painted green and the remaining is painted white. Find the percentage of the area painted in white.

Explanation

To solve the problem step by step, we need to find the percentage of the area painted white on a square sheet with a total area of 250 sq. cm. Here’s how we can do it:

### Step 1: Calculate the area painted red
We know that one-fourth of the sheet is painted red.

\[ \text{Area painted red} = \frac{1}{4} \times \text{Total Area} = \frac{1}{4} \times 250 = 62.5 \text{ sq. cm} \]

### Step 2: Calculate the area left after painting red
Now, we need to find out how much area is left after painting the red area.

\[ \text{Area left} = \text{Total Area} - \text{Area painted red} = 250 - 62.5 = 187.5 \text{ sq. cm} \]

### Step 3: Calculate the area painted green
Next, we know that half of the remaining area is painted green.

\[ \text{Area painted green} = \frac{1}{2} \times \text{Area left} = \frac{1}{2} \times 187.5 = 93.75 \text{ sq. cm} \]

### Step 4: Calculate the area left after painting green
Now, we find out how much area is left after painting the green area.

\[ \text{Area left} = \text{Area left after red} - \text{Area painted green} = 187.5 - 93.75 = 93.75 \text{ sq. cm} \]

### Step 5: Calculate the area painted white
The remaining area is painted white.

\[ \text{Area painted white} = \text{Area left after green} = 93.75 \text{ sq. cm} \]

### Step 6: Calculate the percentage of the area painted white
Finally, we need to find the percentage of the area that is painted white.

\[ \text{Percentage of area painted white} = \left(\frac{\text{Area painted white}}{\text{Total Area}}\right) \times 100 = \left(\frac{93.75}{250}\right) \times 100 \]

Calculating this gives:

\[ \text{Percentage of area painted white} = 37.5\% \]

### Final Answer
The percentage of the area painted in white is **37.5%**.

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