MODEL-8
15. The average age of 20 boys in a class is 15 years. If t
teacher's age is included then the average age is
increased by 2 years. What is the teacher's age?
Answers
Answer:
The teacher's age is 57 years.
Step-by-step explanation:
Given that:
The average age of 20 boys in a class is 15 years.
If the teacher's age is included then the average age is
increased by 2 years.
To Find:
What is the teacher's age?
Let us assume:
The teacher's age be x years.
Formula used:
Average = (Sum of observations)/(Number of observations)
First find the sum of observations:
Average = (Sum of observations)/(Number of observations)
⟶ 15 = (Sum of observations)/(20)
⟶ Sum of observations = 15 × 20
⟶ Sum of observations = 300
When teacher's age is included:
Sum of observations = 300 + x
Number of observations = 20 + 1 = 21
Average = 15 + 2 = 17 years
Now finding the age of teacher:
Average = (Sum of observations)/(Number of observations)
Substituting the values.
⇒ 17 = (300 + x)/21
⇒ 300 + x = 21 × 17
⇒ 300 + x = 357
⇒ x = 357 - 300
⇒ x = 57
∴ The teacher's age = 57 years.
Step-by-step explanation:
Given :-
The average age of 20 boys in a class is 15 years.
The teacher age is included then the average age is increased by 2 years.
To Find :-
What is the teacher's age.
Formula Used :-
\begin{gathered} \longmapsto \sf\boxed{\bold{\pink{Average =\: \dfrac{The\: Sum\: Of\: The\: Observations}{Total\: Number\: Of\: Observations}}}}\\ \end{gathered}
⟼
Average=
TotalNumberOfObservations
TheSumOfTheObservations
Solution :-
\mapsto \sf\bold{\green{In\: the\: first\: case :-}}↦Inthefirstcase:−
Given :
Average age = 15 years
Total boys = 20 years
According to the question by using the formula we get,
↦ \sf 15 =\: \dfrac{Sum\: Of\: The\: Observations}{20}15=
20
SumOfTheObservations
By doing cross multiplication we get,
↦ \sf Sum\: Of\: The\: Observations =\: 20 \times 15SumOfTheObservations=20×15
➦ \sf\bold{\purple{Sum\: Of\: The\: Observations =\: 300}}SumOfTheObservations=300
Hence, the sum of the observation is 300.
\rule{300}{2}
\mapsto \sf\bold{\green{In\: the\: second\: case\: :-}}↦Inthesecondcase:−
Let, the teacher age be x years
Given :
Sum of observations = x + 300
Total number = 20 boys + 1 teacher = 21
Average age = 15 years + 2 years = 17 years
According to the question by using the formula we get,
⇒ \sf 17 =\: \dfrac{x + 300}{21}17=
21
x+300
By doing cross multiplication we get,
⇒ \sf x + 300 =\: 21 \times 17x+300=21×17
⇒ \sf x + 300 =\: 357x+300=357
⇒ \sf x =\: 357 - 300x=357−300
➠ \sf\bold{\red{x =\: 57\: years}}x=57years
\therefore∴ The teacher's age is 57 years.