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

Hint:

First back-calculate the original number of children from the 12% growth, subtract that from the total to get men plus women, then use the after-growth total to set up one equation in one unknown.

Answer 1

The Correct Option is A

Step 1: Find the number of children before the survey.
Children grew by 12% to reach 91,840, so if C is the original number of children, \[ 1.12C = 91840 \] \[ C = \frac{91840}{1.12} = 82000 \]

Step 2: Find the combined men + women population before the survey.
The total population before the survey was 5.477 lakh = 5,47,700. Subtracting children: \[ M+W = 547700-82000 = 465700 \] where M is men and W is women before the survey.

Step 3: Write the equation for the population after one year.
After one year, total population = 6.0466 lakh = 6,04,660, and children after growth = 91,840. So men plus women after one year: \[ 1.08M + 1.125W = 604660 - 91840 = 512820 \]

Step 4: Substitute W in terms of M.
From Step 2, \(W = 465700-M\). Substituting: \[ 1.08M + 1.125(465700-M) = 512820 \] \[ 1.08M + 523912.5 - 1.125M = 512820 \] \[ -0.045M = 512820-523912.5 = -11092.5 \]

Step 5: Solve for M. \[ M = \frac{-11092.5}{-0.045} = 246500 \]

Final Answer:
The population of men before the survey was 246500. \[ \boxed{246500} \]