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 (which corresponds to Option 30).

Step-by-step Explanation:

Step 1: Understand the formula for average
The average of a set of numbers is given by the formula:

$\text{Average}=\frac{\text{Sum of all values}}{\text{Total number of values}}$

Step 2: Calculate the total age of all 4 persons
We are given that the average age of 4 persons (A, B, C, and D) is 25 years.

$\text{Total age of A, B, C, and D}=\text{Average age}\times \text{Total number of persons}$

$\text{Total age}=25\times 4=100\text{years}$

Step 3: Calculate the combined age of A, B, and C
The individual ages of A, B, and C are given as 20 years, 24 years, and 26 years respectively.

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

Step 4: Find the age of D
To find the age of D, subtract the combined age of A, B, and C from the total age of all 4 persons:

$\text{Age of D}=\text{Total age of 4 persons}-\text{Sum of ages of A, B, and C}$

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

Therefore, the age of D is 30 years.