Question

A survey on population growth was conducted in town A. It revealed that the population of the town was 5.477 lakh. In one year, there is an increase in men (aged above 18 years) population by 8%, increase in population of women (aged above 18 years) by 12.5% and increase in the population of children (boy or a girl aged less or equal to 18 years) by 12%. If the population of town A, after one year was found to be 6.0466 lakh and number of children was found to be 91,840, then what was the population of men in the town before survey?

• A. 246500
• B. 256400
• C. 268400
• D. 272600
• E. 289450

Hint:

First isolate the children's original count from the 12% growth, then set up two equations in men and women and eliminate one variable.

Answer 1

The Correct Option is A

Let the population of men, women and children before the survey be \(M\), \(W\) and \(C\) respectively, with \(M+W+C = 547700\) (since 5.477 lakh = 547700).
Children increased by 12% and the new count of children is 91,840, so \(1.12C = 91840\), giving \(C = 82000\).
So \(M + W = 547700 - 82000 = 465700\).
The total population after one year is 6.0466 lakh = 604660. Removing the new children count, \(1.08M + 1.125W = 604660 - 91840 = 512820\).
Since \(W = 465700 - M\), substitute:
\[1.08M + 1.125(465700 - M) = 512820\]
\[1.08M + 523912.5 - 1.125M = 512820\]
\[-0.045M = -11092.5\]
\[M = 246500\]
So the population of men in the town before the survey was 246500.