The average age of a teacher and three students is 20 years. If all the three students are of same age and…
The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?
25 years
30 years
35 years
45 years
Solution
Let the student's age be $s$ and teacher's age be $t = s + 20$. Total of four ages $= 4 \times 20 = 80$. So $t + 3s = 80$, i.e. $(s+20) + 3s = 80$, giving $4s = 60$, $s = 15$. Teacher's age $t = 15 + 20 = 35$ years.