A company was incorporated on 30.4.2007 to acquire the business of a private firm as from 1.1.2007. the company closes its accounts books on 31.12.2007. The sales for the month of august was 3 times of the average , it was twice for January and July, it was 1½ times for October and December and it was ½ of the average sales for November . Illustrate the weighted sales ratio. Assume that the accounting year is from 1st January 2007 to 31st December 2007.

The problem is about determining the weighted sales ratio for a company that acquired a business starting from January 1, 2007, but was incorporated on April 30, 2007. The company closes its accounts on December 31, 2007, and certain months have sales at multiples of an "average" level, while other months have fractions of the average.

### Assumptions:
- The **average sales** refer to the normal level of sales that the company would have in a typical month.
- The year is divided into two periods:
  1. **Pre-incorporation period**: From January 1, 2007, to April 30, 2007.
  2. **Post-incorporation period**: From May 1, 2007, to December 31, 2007.
  
The task is to determine the weighted sales ratio for these periods.

### Step-by-Step Breakdown:

1. **Total months:**
   - Pre-incorporation period: January 1, 2007, to April 30, 2007 (4 months).
   - Post-incorporation period: May 1, 2007, to December 31, 2007 (8 months).

2. **Average monthly sales:**
   Let the **average monthly sales** be represented by \( x \).

3. **Sales ratios for specific months:**
   - **January**: Sales are twice the average, \( 2x \).
   - **July**: Sales are twice the average, \( 2x \).
   - **August**: Sales are three times the average, \( 3x \).
   - **October and December**: Sales are 1.5 times the average for both months, \( 1.5x \).
   - **November**: Sales are half of the average, \( 0.5x \).

4. **Pre-incorporation period sales:**
   Pre-incorporation period consists of the months January to April. So, for these months:
   - January: \( 2x \)
   - February: \( x \) (average sales)
   - March: \( x \) (average sales)
   - April: \( x \) (average sales)

   Total sales in pre-incorporation period:
   \[
   S_{\text{pre-incorporation}} = 2x + x + x + x = 5x
   \]

5. **Post-incorporation period sales:**
   Post-incorporation period consists of May to December. For these months:
   - May: \( x \)
   - June: \( x \)
   - July: \( 2x \)
   - August: \( 3x \)
   - September: \( x \)
   - October: \( 1.5x \)
   - November: \( 0.5x \)
   - December: \( 1.5x \)

   Total sales in post-incorporation period:
   \[
   S_{\text{post-incorporation}} = x + x + 2x + 3x + x + 1.5x + 0.5x + 1.5x = 11.5x
   \]

6. **Weighted sales ratio:**
   The weighted sales ratio is the ratio of sales in the pre-incorporation period to the post-incorporation period:
   \[
   \text{Weighted sales ratio} = \frac{S_{\text{pre-incorporation}}}{S_{\text{post-incorporation}}} = \frac{5x}{11.5x} = \frac{5}{11.5} = \frac{10}{23}
   \]

### Conclusion:
The weighted sales ratio for pre-incorporation to post-incorporation is \( \frac{10}{23} \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How do you calculate the sales for a given month if the average sales value is known?
2. How can the weighted sales ratio affect business decisions?
3. What impact might varying sales multiples have on financial forecasting?
4. How does the length of the pre-incorporation and post-incorporation periods affect the ratio?
5. Can a weighted sales ratio be used to assess company growth over time?

**Tip**: In financial accounting, weighted averages are used to adjust for periods with unequal activity or performance to make comparisons fairer.

A company was incorporated on 30.4.2007 to acquire the business of a private firm as from 1.1.2007. The company closes its accounts books on 31.12.2007. The sales for the month of August were 3 times the average, it was twice for January and July, it was 1½ times for October and December, and it was ½ of the average sales for November. Illustrate the weighted sales ratio. Assume that the accounting year is from 1st January 2007 to 31st December 2007.

Learn how to calculate the weighted sales ratio for a company that acquired a business in 2007, accounting for varying sales multiples across months. This problem demonstrates key concepts like sales proportions, weighted ratios, and algebra. Suitable for advanced high school or college students.

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