In a certain year, the population of a city was 18000. If in the next year, the population of males increased by 5% and that of females increased by 7%, and the total population increased to 19200, then what was the ratio of the populations of males and females in that given year?
This questions was previously asked in
ssc cgl 2023 pre
Explanation:
- Initially, let the population of males be \( M \) and that of females be \( F \).
- Total initial population is given as \( M + F = 18000 \).
- In the next year, male population becomes \( M \times 1.05 \) and female population becomes \( F \times 1.07 \).
- New total population is \( M \times 1.05 + F \times 1.07 = 19200 \).
Now, let's solve for \( M \) and \( F \).
\[
1.05M + 1.07F = 19200
\]
\[
M + F = 18000
\]
- By solving these equations simultaneously, we get:
- Subtracting the first equation from 1.05 times the second equation:
\[
1.05(M + F) - (1.05M + 1.07F) = 1.05 \times 18000 - 19200
\]
- Simplifying:
\[
1.05M + 1.05F - 1.05M - 1.07F = 18900 - 19200
\]
\[
-0.02F = -300
\]
\[
F = 15000
\]
- Using \( M + F = 18000 \):
\[
M + 15000 = 18000
\]
\[
M = 3000
\]
- Therefore, the ratio \( M:F = 3000:15000 = 1:5 \).
- Answer: 1:5
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By: Parvesh Mehta