Read the following passage and answer the questions the follow. In a family of five persons A, B, C, D and E, each and everyone loves one another very much. Their birthdays are in different months and on different dates. A remembers that his birthday is between 25th and 30th, of B it is between 20th and 25th, of C it is between 10th and 20th, of D it is between 5th and 10th and of E it is between 1st to 5th of the month, the sum of the date of birth is defined as the addition of the date and the month, for example 12th January will be written as 12/1 and will add to a sum of the date of 13. (Between 25th and 30th includes both 25 and 30).
If it is known that the dates of birth of three of them are even numbers then find maximum average of their sum of the dates of birth.

Options

A. 24.6
B. 15.2
C. 27.6
D. 28

Answer

To solve the problem, we need to determine the maximum average of the sum of the dates of birth for the family members A, B, C, D, and E, given the constraints on their birthdays. Let's break it down step by step.

### Step 1: Identify the Date Ranges
We have the following ranges for each family member's birthday:
- A: Between 25th and 30th (inclusive)
- B: Between 20th and 25th (inclusive)
- C: Between 10th and 20th (inclusive)
- D: Between 5th and 10th (inclusive)
- E: Between 1st and 5th (inclusive)

### Step 2: Determine Possible Even Dates
From the ranges provided, we identify the possible even dates for each member:
- A: 26, 28, 30 (even numbers between 25 and 30)
- B: 20, 22, 24 (even numbers between 20 and 25)
- C: 10, 12, 14, 16, 18, 20 (even numbers between 10 and 20)
- D: 6, 8, 10 (even numbers between 5 and 10)
- E: 2, 4 (even numbers between 1 and 5)

### Step 3: Select Maximum Even Dates
To maximize the average, we will select the highest even dates from each range:
- A: 30
- B: 24
- C: 20
- D: 10
- E: 4

### Step 4: Determine the Corresponding Months
Next, we need to assign months to these dates. To maximize the average sum, we will choose the last five months of the year:
- A: December (12)
- B: November (11)
- C: October (10)
- D: September (9)
- E: August (8)

### Step 5: Calculate the Sum of Dates and Months
Now we calculate the sum of the dates and their corresponding months:
- For A: 30 + 12 = 42
- For B: 24 + 11 = 35
- For C: 20 + 10 = 30
- For D: 10 + 9 = 19
- For E: 4 + 8 = 12

### Step 6: Calculate the Total and Average
Now, we sum these values:
Total = 42 + 35 + 30 + 19 + 12 = 138

Next, we calculate the average:
Average = Total / Number of members = 138 / 5 = 27.6

### Step 7: Round to Maximum Even Number
Since we are looking for the maximum average of the sum of the dates, we round down to the nearest even number, which is 28.

### Final Answer
The maximum average of the sum of the dates of birth is **28**.

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