A rainy day occurs once in every 10 days. Half of the rainy days produce rainbows. What per cent of all the days do not produce rainbow? 

Options

A. `95%`
B. `10%`
C. `50%`
D. `5%`

Answer

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

### Step 1: Determine the total number of days
Let the total number of days be represented as \( X \).

### Step 2: Calculate the number of rainy days
Since a rainy day occurs once every 10 days, the number of rainy days in \( X \) days is:
\[ \text{Number of rainy days} = \frac{X}{10} \]

### Step 3: Calculate the number of rainy days that produce rainbows
According to the problem, half of the rainy days produce rainbows. Therefore, the number of rainy days that produce rainbows is:
\[ \text{Number of rainbows} = \frac{1}{2} \times \frac{X}{10} = \frac{X}{20} \]

### Step 4: Calculate the number of days that do not produce rainbows
To find the number of days that do not produce rainbows, we subtract the number of days with rainbows from the total number of days:
\[ \text{Days without rainbows} = X - \frac{X}{20} \]
To simplify this, we can express \( X \) as \( \frac{20X}{20} \):
\[ \text{Days without rainbows} = \frac{20X}{20} - \frac{X}{20} = \frac{20X - X}{20} = \frac{19X}{20} \]

### Step 5: Calculate the percentage of days that do not produce rainbows
To find the percentage of days that do not produce rainbows, we divide the number of days without rainbows by the total number of days and multiply by 100:
\[ \text{Percentage without rainbows} = \left( \frac{\frac{19X}{20}}{X} \right) \times 100 \]
Here, \( X \) cancels out:
\[ \text{Percentage without rainbows} = \left( \frac{19}{20} \right) \times 100 = 95\% \]

### Final Answer
The percentage of all the days that do not produce rainbows is **95%**.

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