The average age of 4 persons A, B, C, and D is 25 years. The ages of A, B, and C are 20 years, 24 years, and 26 years respectively. Find the age of D (in years).

The correct answer is 30.

Step-by-step Explanation:

Step 1: Understand the given data

Number of persons = 4 (A, B, C, and D)

Average age of 4 persons = 25 years

Age of A = 20 years

Age of B = 24 years

Age of C = 26 years

Step 2: Calculate the total age of all 4 persons

The formula for the average is:

$\text{Average}=\frac{\text{Total Sum of Ages}}{\text{Total Number of Persons}}$

Rearranging the formula to find the Total Sum of Ages:

$\text{Total Sum of Ages}=\text{Average}\×\text{Total Number of Persons}$

Substituting the given values:

$\text{Total Age of A, B, C, and D}=25\×4=100\text{years}$

Step 3: Calculate the sum of ages of A, B, and C

$\text{Sum of ages of A, B, and C}=20+24+26=70\text{years}$

Step 4: Find the age of D

Subtract the combined age of A, B, and C from the total age of all 4 persons:

$\text{Age of D}=\text{Total Age}-\text{Sum of ages of (A + B + C)}$

$\text{Age of D}=100-70=30\text{years}$

Therefore, the age of D is 30 years.