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saw5 [17]
3 years ago
10

one-third of the people from country A claim that they are from country B, and the rest admit they are from country A. One-fourt

h of the people from country claim that they are from country A, and the rest admit they are from country B. In a combined census of the two countries, one-half of the total claimed to be from A. What is the ratio of the populations of Country A to that of country B.
Mathematics
1 answer:
In-s [12.5K]3 years ago
8 0

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,

 \text{The population of country A that admit they are from B} = \frac{1}{3}\text{ of }A

⇒ \text{ The population of A that admit they are from country A }= A - \frac{1}{3} \text{ of } A

= \frac{3-1}{3} A

= \frac{2}{3} A

\text{The population of country B that admit they are from A} = \frac{1}{4}\text{ of }B

⇒ \text{ The total population that claims that they are from A }= \frac{2}{3} A +\frac{1}{4} B

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.

⇒ \frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}(A+B)

⇒ \frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}A+\frac{1}{2}B

⇒ \frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}A+\frac{1}{2}B

⇒ \frac{2}{3} A - \frac{1}{2}A= \frac{1}{2}B-\frac{1}{4} B

⇒ \frac{4}{6} A - \frac{3}{6}A= \frac{2}{4}B-\frac{1}{4} B

⇒ \frac{1}{6} A = \frac{1}{4} B

⇒ A =\frac{6}{4}B

⇒ \frac{A}{B} =\frac{3}{2}

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