B was born when A was 4 years 7 months old and C was born when B was 3 years 4 months old. When C was 5 years 2 months old, then their average age was

Options

A. 8 years 9 months
B. 7 years 3 months
C. 8 years 7 months
D. 8 years 11 months

Answer

To solve the problem step by step, we will calculate the ages of A, B, and C when C is 5 years and 2 months old, and then find their average age.

### Step 1: Determine A's age when B was born
- B was born when A was 4 years and 7 months old.
- Therefore, A's age at that time = 4 years 7 months.

### Step 2: Determine B's age when C was born
- C was born when B was 3 years and 4 months old.
- Therefore, B's age at that time = 3 years 4 months.

### Step 3: Determine C's age when C is 5 years and 2 months old
- Given that C is currently 5 years and 2 months old.

### Step 4: Calculate A's current age when C is 5 years and 2 months
- Since B was 3 years and 4 months old when C was born, we can find B's current age:
- B's current age = B's age when C was born + C's current age
- B's current age = 3 years 4 months + 5 years 2 months
- Convert the ages to months:
- 3 years 4 months = 40 months
- 5 years 2 months = 62 months
- B's current age in months = 40 + 62 = 102 months
- Convert back to years and months: 102 months = 8 years 6 months.

- Now, we can find A's current age:
- A's current age = A's age when B was born + B's current age
- A's current age = 4 years 7 months + 8 years 6 months
- Convert the ages to months:
- 4 years 7 months = 55 months
- 8 years 6 months = 102 months
- A's current age in months = 55 + 102 = 157 months
- Convert back to years and months: 157 months = 13 years 1 month.

### Step 5: Calculate the average age of A, B, and C
- Now we have:
- A's current age = 13 years 1 month
- B's current age = 8 years 6 months
- C's current age = 5 years 2 months

- Convert all ages to months for easy calculation:
- A's age in months = 13 * 12 + 1 = 157 months
- B's age in months = 8 * 12 + 6 = 102 months
- C's age in months = 5 * 12 + 2 = 62 months

- Now, calculate the total age in months:
- Total age = 157 + 102 + 62 = 321 months

- Calculate the average age:
- Average age in months = Total age / Number of people = 321 / 3 = 107 months

### Step 6: Convert the average age back to years and months
- Convert 107 months to years and months:
- 107 months = 8 years and 11 months.

### Final Answer
The average age of A, B, and C when C is 5 years and 2 months old is **8 years and 11 months**.

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