Among four students sitting in a row, average age of last three students is 20 years and the average age of first three students is 21 years. If the age of first student is 26 years, then what is the age (in years) of the last student?

Options

A. 23
B. 37
C. 24
D. 29

Answer

To solve the problem, we will denote the ages of the four students as follows:

- Let the age of the first student (A) be \( A = 26 \) years.
- Let the age of the second student (B) be \( B \) years.
- Let the age of the third student (C) be \( C \) years.
- Let the age of the fourth student (D) be \( D \) years.

### Step 1: Calculate the total age of the last three students (B, C, D)
The average age of the last three students (B, C, D) is given as 20 years. Therefore, we can express this mathematically as:

\[ \frac{B + C + D}{3} = 20 \]

To find the total age of B, C, and D, we multiply both sides by 3:

\[ B + C + D = 20 \times 3 = 60 \]

### Step 2: Calculate the total age of the first three students (A, B, C)
The average age of the first three students (A, B, C) is given as 21 years. Therefore, we can express this mathematically as:

\[ \frac{A + B + C}{3} = 21 \]

Substituting \( A = 26 \) into the equation gives us:

\[ \frac{26 + B + C}{3} = 21 \]

To find the total age of A, B, and C, we multiply both sides by 3:

\[ 26 + B + C = 21 \times 3 = 63 \]

### Step 3: Solve for B + C
Now we can isolate \( B + C \):

\[ B + C = 63 - 26 = 37 \]

### Step 4: Substitute B + C into the equation for B + C + D
We already found that:

\[ B + C + D = 60 \]

Now we can substitute \( B + C = 37 \) into this equation:

\[ 37 + D = 60 \]

### Step 5: Solve for D
To find the age of the last student (D), we can rearrange the equation:

\[ D = 60 - 37 = 23 \]

### Conclusion
The age of the last student (D) is **23 years**.

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