Question

In a school of 1600 students, the ratio of teachers to students is 1:16.

Some teachers join the school and the ratio changes to 3:40.

Find the number of teachers who joined the school.

Answer 1

Answer:

The number of teacher who joined the school is 20

Step-by-step explanation:

Teacher : Students = 1 : 16

Number of teachers = 1x

Number of students = 16x

16x = 1600

x = 1600/16

x = 100

Number of teachers at the beginning = 100

Now, after some teachers (let it be y) joining the school,

Teacher : students = 3:40

$\frac{100+y}{1600}=\frac{3}{40}\\\\40*(100+y)=3*1600\\\\4000+40y = 4800\\\\40y=4800-4000\\\\40y=800\\\\y=\frac{800}{40}\\\\y=20$

The number of teacher who joined the school is 20