Question

a) There are 15 teachers in a school and 10 of them are male teachers. i) Find the ratio of the number of male and female teachers. (ii) Find the ratio of the number of female teachers and the total number of teachers. One of the angles of a pair of complementary angles is 50°. Find the ratio of the pair of complementary angles.​

Answer 1

Explanation:

Total number of teachers = 15

Given number of male teachers = 10

Therefore number of female teachers = 15 - 10 = 5

i)

Ratio of male and female teachers

`(male)/(female) = (10)/(5) = (2)/(1)\\\\Ratio = 2 : 1`

ii)

Ratio of female teachers and total number of teachers

`(female)/(total\ teachers) = (5)/(15) =(1)/(3) \\\\Ratio = 1 : 3`

iii)

If x and y are complementary angles, then x+ y = 90°

Given : one angle, x = 50°

Therefore, 50° + y = 90°

y = 90 - 50 = 40°

Ratio of the pair of complementary angles

`(x)/(y) = (50)/(40) = (5)/(4) \\\\Ratio = 5 : 4`

Answer 2

i) 2:1

ii) 1:3

iii) 5:4

Explanation:

i) Male teachers : Female teachers

10 : 15-10

10 : 5

2 : 1

ii) Female teachers : Total teachers

5 : 15

1 : 3

iii) Do remember that two angles are called complementary if their measures add to 90 degrees.

Hence, ration of the pair of complementary angles = 50 : 90-50

= 50 : 40

= 5 : 4