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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
This Question has 1 answers.
$ \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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