Five years ago, the average of the ages of 4 persons was 40 years. If a new person joins the group now, then the average of the ages all five persons is 46 years. The age of the fifth person (in years) is:

Options

A. 50
B. 55
C. 48
D. 47

Answer

To find the age of the fifth person, we can break down the problem step by step.

### Step 1: Calculate the total age of the 4 persons 5 years ago.
Given that the average age of 4 persons 5 years ago was 40 years, we can find the total age of these 4 persons at that time.

\[ \text{Total age of 4 persons 5 years ago} = \text{Average age} \times \text{Number of persons} = 40 \times 4 = 160 \text{ years} \]

### Step 2: Calculate the total age of the 4 persons now.
Since 5 years have passed, each of the 4 persons has aged 5 years. Therefore, we can calculate their total age now.

\[ \text{Total age of 4 persons now} = \text{Total age 5 years ago} + (5 \times 4) = 160 + 20 = 180 \text{ years} \]

### Step 3: Calculate the total age of all 5 persons now.
We know that the average age of all 5 persons now is 46 years. Therefore, we can find the total age of all 5 persons.

\[ \text{Total age of 5 persons now} = \text{Average age} \times \text{Number of persons} = 46 \times 5 = 230 \text{ years} \]

### Step 4: Calculate the age of the fifth person.
Now, we can find the age of the fifth person by subtracting the total age of the 4 persons from the total age of all 5 persons.

\[ \text{Age of the 5th person} = \text{Total age of 5 persons now} - \text{Total age of 4 persons now} = 230 - 180 = 50 \text{ years} \]

Thus, the age of the fifth person is **50 years**.

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