Question

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?
​

Answer 1

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.

Answer 2

Answer:

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 :-

$\longmapsto \sf\boxed{\bold{\pink{Average =\: \dfrac{The\: Sum\: Of\: The\: Observations}{Total\: Number\: Of\: Observations}}}}$

Solution :-

$\mapsto \sf\bold{\green{In\: the\: first\: case :-}}$

Given :

• Average age = 15 years
• Total boys = 20 years

According to the question by using the formula we get,

↦ $\sf 15 =\: \dfrac{Sum\: Of\: The\: Observations}{20}$

By doing cross multiplication we get,

↦ $\sf Sum\: Of\: The\: Observations =\: 20 \times 15$

➦ $\sf\bold{\purple{Sum\: Of\: The\: Observations =\: 300}}$

Hence, the sum of the observation is 300.

$\rule{300}{2}$

$\mapsto \sf\bold{\green{In\: the\: second\: case\: :-}}$

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,

⇒ $\sf 17 =\: \dfrac{x + 300}{21}$

By doing cross multiplication we get,

⇒ $\sf x + 300 =\: 21 \times 17$

⇒ $\sf x + 300 =\: 357$

⇒ $\sf x =\: 357 - 300$

➠ $\sf\bold{\red{x =\: 57\: years}}$

$\therefore$ The teacher's age is 57 years.