Question:hard

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?

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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.
Updated On: Jul 21, 2026
  • 246500
  • 256400
  • 268400
  • 272600
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The Correct Option is A

Solution and Explanation

Step 1: Work with the increase amounts instead of the final totals.
The total population increase over the year is \[ 604660-547700 = 56960 \]

Step 2: Find how much of that increase came from children.
Original children \(=91840/1.12=82000\), so the increase in children is \[ 91840-82000 = 9840 \]

Step 3: Find the combined increase from men and women.
Subtracting the children's increase from the total increase: \[ 56960 - 9840 = 47120 \] This means \(0.08M + 0.125W = 47120\), since the increase from men is 8% of M and from women is 12.5% of W.

Step 4: Use the men-plus-women total from before the survey. \[ M+W = 547700-82000 = 465700 \] so \(W=465700-M\).

Step 5: Substitute and solve. \[ 0.08M+0.125(465700-M) = 47120 \] \[ 0.08M + 58212.5 - 0.125M = 47120 \] \[ -0.045M = 47120-58212.5 = -11092.5 \] \[ M = \frac{11092.5}{0.045} = 246500 \]
Working from the increase amounts rather than the after-growth totals gives the same figure, confirming the population of men before the survey. \[ \boxed{246500} \]
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