Average age of 20 students is 21 years. 2 students leave the group and 1 new student joins the group. The average now becomes 20 years. If age of one of the student who left the group is 26 years and the one who joined is 20 years, then what is the age (in years) of the other student who left the group?a)24b)34c)22d)36Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
- Average age of 20 students = 21 years
- 2 students leave the group and 1 new student joins the group
- The average now becomes 20 years
- Age of one of the student who left the group is 26 years and the one who joined is 20 years

To find:
- Age of the other student who left the group

Solution:
Let the sum of ages of 20 students be 'x'
So, the average age of 20 students = x/20 = 21
=> x = 20 * 21 = 420

Now, 2 students leave the group and 1 new student joins the group.
So, the total number of students = 20 - 2 + 1 = 19

Let the age of the other student who left the group be 'y'

According to the question, the new average age of 19 students is 20 years
So, the sum of ages of 19 students = 19 * 20 = 380

Also, we know that the sum of ages of (18 students who were there initially + the new student who joined) is (sum of ages of 20 students who were there initially - age of the student who left + age of the new student who joined)
=> (sum of ages of 18 students + age of new student) = (420 - 26 + 20) = 414

Now, we can form an equation using the above values:
(sum of ages of 18 students) + y + 20 = 414
=> (sum of ages of 18 students) + y = 394

Also, we know that (sum of ages of 18 students) = (sum of ages of 20 students who were there initially) - (age of the student who left)
=> (sum of ages of 18 students) = (420 - 26)
=> (sum of ages of 18 students) = 394

Substituting this value in the previous equation, we get:
394 + y = 394
=> y = 0

Therefore, the age of the other student who left the group is 0 years.

Answer: Option B (34) is not correct.

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