Question

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
(i) the initial number of teachers in the school,
(ii) the number of teachers who join the school.​

Answer 1

No. Of Teachers Initially = 80
No. of Teachers joined = 10

Answer 2

Explanation:

i)Initial School population,

given 15 units = 1200

1 unit =

`1200 / 15 \\ = 80`

Number of teachers (initial) = 1 unit = 80.

ii)take j = number of teachers joining the school.

New teacher population = 80+j

`(3)/(43) (1280 + j) = 80 + j \\ (3840)/(43) + (3)/(43) j = 80 + j \\ j - (3)/(43) j = (3840)/(43) - 80 \\ (40)/(43) j = (400)/(43) \\ 40j = 400 \\ j = 400 / 40 \\ = 10`