JEE MAIN - Mathematics (2021 - 18th March Morning Shift - No. 20)
The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is _________.
답변
35
설명
Mean $$\left( {\overline x } \right)$$ = $${{{x_1} + {x_2}..... + {x_n}} \over n}$$ = $${{\sum x } \over n}$$
Here, Mean = 40 of 25 teachers
$$\therefore$$ 40 = $${{\sum x } \over {25}}$$
$$ \Rightarrow $$ $$\sum x $$ = 40 $$ \times $$ 25 = 1000
After retireing of a 60 year old teacher, total age of 24 teachers,
x1 + x2 + . . . . . .x24 = 1000 $$-$$ 60 = 940
Now a new teacher of age A year is appointed.
$$\therefore$$ Now total age of this 25 teachers
x1 + x2 + x3 + . . . . . + x25 = 940 + A
$$\therefore$$ Mean age = $${{940 + A} \over {25}}$$
According to question,
$${{940 + A} \over {25}}$$ = 39
$$ \Rightarrow $$ A = 35
Here, Mean = 40 of 25 teachers
$$\therefore$$ 40 = $${{\sum x } \over {25}}$$
$$ \Rightarrow $$ $$\sum x $$ = 40 $$ \times $$ 25 = 1000
After retireing of a 60 year old teacher, total age of 24 teachers,
x1 + x2 + . . . . . .x24 = 1000 $$-$$ 60 = 940
Now a new teacher of age A year is appointed.
$$\therefore$$ Now total age of this 25 teachers
x1 + x2 + x3 + . . . . . + x25 = 940 + A
$$\therefore$$ Mean age = $${{940 + A} \over {25}}$$
According to question,
$${{940 + A} \over {25}}$$ = 39
$$ \Rightarrow $$ A = 35