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).
What may be the minimum average of their sum of the dates of births?

Options

A. 24.6
B. 15.2
C. 28
D. 32

Answer

To find the minimum average of the sum of the dates of birth for the family members A, B, C, D, and E, we need to follow these steps:

### Step 1: Identify the Range of Dates for Each Person
- A's birthday is between 25th and 30th: **Minimum = 25**
- B's birthday is between 20th and 25th: **Minimum = 20**
- C's birthday is between 10th and 20th: **Minimum = 10**
- D's birthday is between 5th and 10th: **Minimum = 5**
- E's birthday is between 1st and 5th: **Minimum = 1**

### Step 2: Assign Months to Each Birthday
To minimize the average, we will assign the earliest months to the earliest dates:
- A (25th) - **January** (Month = 1)
- B (20th) - **February** (Month = 2)
- C (10th) - **March** (Month = 3)
- D (5th) - **April** (Month = 4)
- E (1st) - **May** (Month = 5)

### Step 3: Calculate the Sum of Dates and Months
Now we calculate the sum of the dates and the corresponding months:
- A: 25 (date) + 1 (month) = 26
- B: 20 (date) + 2 (month) = 22
- C: 10 (date) + 3 (month) = 13
- D: 5 (date) + 4 (month) = 9
- E: 1 (date) + 5 (month) = 6

### Step 4: Total the Sums
Now we add these sums together:
- Total = 26 + 22 + 13 + 9 + 6 = 76

### Step 5: Calculate the Average
To find the average, we divide the total by the number of family members:
- Average = Total Sum / Number of Persons = 76 / 5 = 15.2

### Conclusion
The minimum average of their sum of the dates of births is **15.2**.

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