Question

The average of 20 students class is 21. If the age of teacher is included then average increase by 2yr. Find age of teacher? 20 छात्रों की कक्षा का औसत 21 है। यदि शिक्षक की आयु को शामिल किया जाए तो औसत 2 साल की वृद्धि होती है। शिक्षक की आयु ज्ञात कीजिये?​

Answer 1

${{ \text{ \underline{ { \underline{Given data}}}}}:-}$

• The average age of 20 students class is 21.
• The age of teacher is included then average increase by 2yr.

${{ \text{ \underline{ { \underline{Solution}}}}}:-}$

Let, age of 20 students be x and age of teacher be y.

Formula:

${ \dashrightarrow{ \tt{Average = \frac{Sum \: of \: the \: terms}{Number \: of \: terms} }}}$

{According to given}

Now, for age of students.

${ \dashrightarrow{ \bf{ \frac{x}{20} = 21 }}}$

${ \dashrightarrow{ \bf{ {x}= 21 \times 20 }}}$

${ \dashrightarrow{ \bf{ {x}= 420 }} \: \: \: \: \: \: \: \: \: ....(1)}$

{According to given}

When, the age of teacher is included then average increase by 2yr.

${ \dashrightarrow{ \bf{ \frac{x + y}{20 + 1} = 21 + 2 }}}$

{from ( 1 )}

${ \dashrightarrow{ \bf{ \frac{420 + y}{21} = 23 }}}$

${ \dashrightarrow{ \bf{ {420 + y} = 23 \times 21}}}$

${ \dashrightarrow{ \bf{ {420 + y} = 483}}}$

${ \dashrightarrow{ \bf{ { y} = 483 - 420}}}$

${ \dashrightarrow{ \bf{ { y} = 63 \: years}}}$

Hence, the age of teacher is 63 years.