Question
In a coaching institute, there are 80 mathematics
teachers, 60 English teachers, 100 physics teachers, and 40 chemistry teachers. The ratio of male to female mathematics teachers in the institute is 3:1, and the ratio of male to female English teachers is 2:1. Within the physics department, the number of male teachers exceeds the number of female teachers by 20. Furthermore, half of the teachers in the chemistry department are male. Determine the ratio of the total number of male to female teachers in the institute.Solution
ATQ, we can say that Male Mathematics Teachers = 80 × ¾ = 60 Female Mathematics Teachers = 80 × ¼ = 20 Male English Teachers = 2/3 × 60 = 40 Female English Teachers = 1/3 × 60 = 20 Male Teachers in Physics = 40 + 20 = 60 Female Teachers in Physics = 40 Male Teachers in Chemistry = 40/2 = 20 Female Teachers in Chemistry = 40/2 = 20 Required ratio = (60 + 40 + 60 + 20):(20 + 20 + 40 + 20) = 180:100 = 9:5
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