Given:
In a town, 30% were children, while 45% were men. 25000 women were there at some time.
In the next 5 years, 10% men and 5% women became old and dead, whereas 6% of children were grown as men and 4% of children were grown as women.
1000 children were added to the list.
Calculations:
Let the population of town be x
30% were children, 45% were men. So, the remaining are the women = 100 - (45 + 30) = 100 - 75 = 25%
So, total population of town is 25% of x = 25000
\(\dfrac{25}{100}\) of x = 25000
x = \(\dfrac{25000 × 100}{25}\) = 100000
Number of men = 45% of 100000 = \(\dfrac{45}{100}\) of 100000 = 45000
Number of children = 30% of 100000 = \(\dfrac{30}{100}\)of 100000 = 30000
Now, after 5 years,
10% men become old and dead = 45000 × 10% = 45000 × \(\dfrac{10}{100}\) = 4500
6% of children were grown as men = \(\dfrac{6}{100}\) of 30000 = 1800
So, number of men left = 45000 - 4500 + 1800 = 42300
5% women become old and dead = 25000 × 5% = 25000 - \(\dfrac{5}{100}\) = 1250
and 4% of children were grown as women = \(\dfrac{4}{100}\) of 30000 = 1200
So, number of women left = 25000 - 1250 + 1200= 24950
And, 1000 children were added.
Number of children = 30000 + 1000 - 1200 (were grown as women - 1800(were grown as men) = 28000
So, total number of new population = number of men + number of children + number of women = 42300 + 24950 + 28000 = 95250
∴ The answer is 95250.
Alternate MethodLet the total population be 100x,
Children among 100x = 30x
Men among 100x = 45x
and remaining are Women = 100x - 30x - 45x = 25x,
Now according to the question,
25x = 25,000
⇒ x = 25,000/25 = 1,000
10% of men and 5% of women died,
The remaining men and women are,
⇒ Men = 45x - 10% of 45x = 45x - 4.5x = 40.5x
⇒ Women = 25x - 5% of 25x = 25x - 1.25x = 23.75x
Now 6% of children grow as men,
6% of 30 = 1.8x
Total men = 40.5x + 1.8x = 42.3x
and 4% of children grow as women,
4% of 30 = 1.2x
Total women = 23.75x + 1.2x = 24.95x
Total children = 30x - 1.8x - 1.2x = 27x
Total current population,
⇒ 42.3x + 24.95x + 27x = 94.25x
We have the value of x as 1,000
⇒ 94.25 × 1,000 = 94250
but in the last line of the question, we have, 1000 children are also added
Thus, total population = 94250 + 1000 = 95250
∴ Total population is 95,250.