In a colony of 70 residents, the ratio of the number of men and women is 4:3.

In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?

A). 1:2

B). 3:4

C). 1:4

D). 1:3

$ \text{Let the number of men} = 4x, \quad \text{Let the number of women} = 3x $

$ 4x + 3x = 70 $

$ x = 10 $

$ \text{Number of men} = 40, \quad \text{Number of women} = 30 $

$ \text{Let the number of educated women} = y, \quad \text{Uneducated women} = 4y $

$ y + 4y = 30 $

$ y = 6 $

$ \text{Educated women} = 6, \quad \text{Uneducated women} = 24 $

$ \text{Let the number of educated men} = E_m, \quad \text{Let the number of uneducated men} = U_m $

$ E_m + U_m = 40 $

$ \frac{E_m + 6}{U_m + 24} = \frac{8}{27} $

$ (E_m + 6) \times 27 = (U_m + 24) \times 8 $

$ 27E_m + 162 = 8U_m + 192 $

$ 27E_m - 8U_m = 30 $

$ U_m = 40 - E_m $

$ 27E_m - 8(40 - E_m) = 30 $

$ 27E_m - 320 + 8E_m = 30 $

$ 35E_m = 350 $

$ E_m = 10 $

$ U_m = 40 - 10 = 30 $

$ \text{Ratio of educated men to uneducated men} = 10:30 = 1:3 $

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