Respuesta :
Answer: 3 : 2
Step-by-step explanation:
Let A represents the total population of country A and B represents the total population of country B.
According to the question,
[tex]\text{The population of country A that admit they are from B} = \frac{1}{3}\text{ of }A[/tex]
⇒ [tex]\text{ The population of A that admit they are from country A }= A - \frac{1}{3} \text{ of } A[/tex]
[tex] = \frac{3-1}{3} A[/tex]
[tex] = \frac{2}{3} A[/tex]
[tex]\text{The population of country B that admit they are from A} = \frac{1}{4}\text{ of }B[/tex]
⇒ [tex]\text{ The total population that claims that they are from A }= \frac{2}{3} A +\frac{1}{4} B[/tex]
But, Again according to the question,
The total population that claims that they are from A = one half of the total population of A and B.
⇒ [tex]\frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}(A+B)[/tex]
⇒ [tex]\frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}A+\frac{1}{2}B[/tex]
⇒ [tex]\frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}A+\frac{1}{2}B[/tex]
⇒ [tex]\frac{2}{3} A - \frac{1}{2}A= \frac{1}{2}B-\frac{1}{4} B[/tex]
⇒ [tex]\frac{4}{6} A - \frac{3}{6}A= \frac{2}{4}B-\frac{1}{4} B[/tex]
⇒ [tex]\frac{1}{6} A = \frac{1}{4} B[/tex]
⇒ [tex]A =\frac{6}{4}B[/tex]
⇒ [tex]\frac{A}{B} =\frac{3}{2}[/tex]
