
The average age of a teacher and three students is 20 years. If all the students are of equal age and the difference between the age of the teacher and that of a student is 20 years, then the age of the teacher is
A. 25 years
B. 30 years
C. 35 years
D. 45 years
Answer
472.5k+ views
Hint: First of all this is a very simple and a very easy problem. This problem deals with algebraic mathematics. Here given the arithmetic mean of the ages of a teacher and three students. We are asked to find the age of the teacher. Here in any given data the arithmetic mean of the data is given by the ratio of sum of all the given observations in the data to the total number of observations.
The average of the given data , is given by:
Complete step-by-step answer:
Given that there is a teacher and three students.
The three students are of the same age, but the teacher is not.
Given that the average of the ages of the teacher and the three students is 20 years.
Also given that the difference between the age of teacher and the students is 20 years.
Let the age of the teacher =
Let the age of one of the three students =
Now the ages of all the three students is the same, as given.
The average age of the teacher and the three students is 20 years, as mathematically expressed below:
The difference between the age of the teacher and that of a student is 20 years, as given below:
Now substituting the expression for in the obtained expression , as given below:
Expanding the above expression, as given below:
Dividing the above expression with 4, as given below:
Hence the age of the teacher is 35 years.
The age of the teacher is 35 years.
Note:
Please note that this problem can be done in another way which is slightly different from this method, which is described here. As we have obtained 2 equations from the given information, one is and , here instead of solving for by substitution, we could rather solve the both equations for and we can proceed forward, where the final answer will be the same as obtained in the previous method before.
The average of the given data
Complete step-by-step answer:
Given that there is a teacher and three students.
The three students are of the same age, but the teacher is not.
Given that the average of the ages of the teacher and the three students is 20 years.
Also given that the difference between the age of teacher and the students is 20 years.
Let the age of the teacher =
Let the age of one of the three students =
Now the ages of all the three students is the same, as given.
The average age of the teacher and the three students is 20 years, as mathematically expressed below:
The difference between the age of the teacher and that of a student is 20 years, as given below:
Now substituting the expression for
Expanding the above expression, as given below:
Dividing the above expression with 4, as given below:
Hence the age of the teacher is 35 years.
The age of the teacher is 35 years.
Note:
Please note that this problem can be done in another way which is slightly different from this method, which is described here. As we have obtained 2 equations from the given information, one is
Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
School Full course for MAHARASHTRABOARD students
₹31,500 per year
Recently Updated Pages
Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Write the following in Roman numerals 25819 class 7 maths CBSE

Trending doubts
State and prove Bernoullis theorem class 11 physics CBSE

What are Quantum numbers Explain the quantum number class 11 chemistry CBSE

Write the differences between monocot plants and dicot class 11 biology CBSE

Who built the Grand Trunk Road AChandragupta Maurya class 11 social science CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

State the laws of reflection of light
