Question

12. In a school of 1200 students, the ratio of
the number of teachers to students is 1 : 15.
After some teachers join the school, the ratio of
the number of teachers to students becomes 3:40.
.Find the initial number of teachers in the school
number of teachers who join the school.
​

Answer 1

Answer:

The initial number of teachers  = 80

The number of teachers who join the school = 10

Step-by-step explanation:

Given,

The number of student in the school = 1200

Ratio of teachers to students initially = 1:15

Ratio of teachers to students after the joining of new teachers  = 3:40

To find

The initial number of teachers

The number of teachers who join the school

Solution:

Since Ratio of teachers to students initially = 1:15,

then the number of teachers initially= x and the number of students  = 15x

Since the number of students = 1200, we have

15x = 1200

x = 80

∴The initial number of teachers  = 80

Since the ratio of teachers to students after the joining of new teachers  = 3:40

Then , the number of teachers = 3x and the number of students = 40x

We have the number of students in the school = 1200

that is 40x = 1200

x = 30

∴The number of teachers after some teacher's joining the school = 3x = 3×3 = 90

∴The number of teachers who join the school = 90 -80 = 10

#SPJ2

Answer 2

Answer:

The initial number of the teachers in the school is 80.

The number of the teachers who join the school is 10.

Step-by-step explanation:

To find:-

(a) The initial number of the teachers in the school.

(b) The number of the teachers who join the school.

Given:-

The total number of the students in a school = 1200

The ratio of the number of the teachers to the students = 1 : 15

Let the common ratio be x.

Then,

The number of the teachers = x

And the number of the students = 15x

(a) Since the total number of students is 1200.

⇒ 15x = 1200

⇒ x = 1200/15

⇒ x = 80

Thus, the initial number of the teachers in the school is 80.

(b) After some teachers join the school,

Then, the new ratio of the number of teachers to the students = 3 : 40

Now, let the common ratio be y.

Then,

The number of the teachers = 3x

And the number of the students = 40x

Since the total number of students is 1200.

⇒ 40x = 1200

⇒ x = 1200/40

⇒ x = 30

So, the number of the teachers = 3 × 30

                                                    = 90

Hence the teachers who join the school = 90 -80

                                                                   = 10

Thus, the number of the teachers who join the school is 10.

#SPJ2