Question

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-fourth 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.

Answer 1

Answer: 3 : 2

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} = (1)/(3)\text{ of }A`

⇒
`\text{ The population of A that admit they are from country A }= A - (1)/(3) \text{ of } A`

`= (3-1)/(3) A`

`= (2)/(3) A`

`\text{The population of country B that admit they are from A} = (1)/(4)\text{ of }B`

⇒
`\text{ The total population that claims that they are from A }= (2)/(3) A +(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.

⇒
`(2)/(3) A + (1)/(4) B= (1)/(2)(A+B)`

⇒
`(2)/(3) A + (1)/(4) B= (1)/(2)A+(1)/(2)B`

⇒
`(2)/(3) A + (1)/(4) B= (1)/(2)A+(1)/(2)B`

⇒
`(2)/(3) A - (1)/(2)A= (1)/(2)B-(1)/(4) B`

⇒
`(4)/(6) A - (3)/(6)A= (2)/(4)B-(1)/(4) B`

⇒
`(1)/(6) A = (1)/(4) B`

⇒
`A =(6)/(4)B`

⇒
`(A)/(B) =(3)/(2)`