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In a certain year, the population of a certain town was 12000. If the next year the population of males increases by 3% and that of the females by 7% and total population increases to 12800, then what was the ratio of population of males and females in that given year ? 
  • a)
    1 : 11
  • b)
    5 : 4
  • c)
    2 : 3
  • d)
    Data inadequate
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
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In a certain year, the population of a certain town was 12000. If the ...
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In a certain year, the population of a certain town was 12000. If the ...
Given:
- Population of the town in a certain year = 12000
- Population of males increases by 3% the next year
- Population of females increases by 7% the next year
- Total population in the next year = 12800

To find:
The ratio of the population of males to females in that given year

Solution:
Let's assume the population of males in the given year is M and the population of females is F.

Step 1: Formulating the equations
- The population of males in the next year will be M + 0.03M = 1.03M
- The population of females in the next year will be F + 0.07F = 1.07F

Step 2: Formulating the equation for the total population in the next year
The total population in the next year is given as 12800, so we can write:
1.03M + 1.07F = 12800

Step 3: Solving the equation
To find the values of M and F, we need to solve the equation 1.03M + 1.07F = 12800.
Since there is only one equation and two variables, we cannot find the exact values of M and F.

Step 4: Finding the ratio of males to females
However, we can find the ratio of M to F.
Dividing both sides of the equation 1.03M + 1.07F = 12800 by F, we get:
(1.03M/F) + 1.07 = 12800/F

Assuming the ratio of M to F as x/y, we can rewrite the equation as:
(1.03x/y) + 1.07 = 12800/(x/y)
(1.03x/y) + 1.07 = (12800y)/x

Cross-multiplying, we get:
1.03x^2 + 1.07xy = 12800y

Since we don't have any other information about the values of x and y, we cannot find their exact values.

However, if we assume the population of females is y = 1, then the equation becomes:
1.03x^2 + 1.07x = 12800
Solving this equation will give us the value of x/y, which represents the ratio of males to females.

Conclusion:
Hence, we cannot determine the exact ratio of the population of males to females without additional information. Therefore, option (d) "Data inadequate" is the correct answer.
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In a certain year, the population of a certain town was 12000. If the next year the population of males increases by 3% and that of the females by 7% and total population increases to 12800, then what was the ratio of population of males and females in that given year ?a)1 : 11b)5 : 4c)2 : 3d)Data inadequatee)None of theseCorrect answer is option 'A'. Can you explain this answer?
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