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The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 is
- a)68.25
- b)68.75
- c)68.50
- d)69.25
Correct answer is option 'B'. Can you explain this answer?
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The total of male and female populations in a city increased by 25% fr...
Calculation of Percentage Increase in Population from 1970 to 1990
- Let's assume the initial populations in 1970 were M males and F females.
- The total population in 1970 is M + F.
- Given that the total population increased by 25% from 1970 to 1980, the total population in 1980 is 1.25(M + F).
- During this period, the male population increased by 40%, so the male population in 1980 is 1.4M, and the female population increased by 20%, so the female population in 1980 is 1.2F.
- Therefore, in 1980, the total population is 1.4M + 1.2F = 1.25(M + F).
- Solving these equations, we get M = F.
Population in 1990
- Given that in 1990, the female population is twice the male population, let the male population in 1990 be x. Therefore, the female population in 1990 is 2x.
- The total population in 1990 is x + 2x = 3x.
- Given that the female population increased by 25% from 1980 to 1990, we have 2x = 1.25(1.2F).
- Solving for x, we get x = 100.
- Therefore, in 1990, the male population is 100, and the female population is 200, making the total population 300.
Percentage Increase in Population from 1970 to 1990
- The total population in 1970 was M + F = 2M, and in 1990, the total population is 3x = 300.
- The percentage increase is (300 - 2M) / 2M * 100 = (300 - 200) / 200 * 100 = 100 / 200 * 100 = 50%.
- Therefore, the percentage increase in the total of male and female populations in the city from 1970 to 1990 is 50%.
Therefore, the correct answer is option 'B' - 68.75%.
- Let's assume the initial populations in 1970 were M males and F females.
- The total population in 1970 is M + F.
- Given that the total population increased by 25% from 1970 to 1980, the total population in 1980 is 1.25(M + F).
- During this period, the male population increased by 40%, so the male population in 1980 is 1.4M, and the female population increased by 20%, so the female population in 1980 is 1.2F.
- Therefore, in 1980, the total population is 1.4M + 1.2F = 1.25(M + F).
- Solving these equations, we get M = F.
Population in 1990
- Given that in 1990, the female population is twice the male population, let the male population in 1990 be x. Therefore, the female population in 1990 is 2x.
- The total population in 1990 is x + 2x = 3x.
- Given that the female population increased by 25% from 1980 to 1990, we have 2x = 1.25(1.2F).
- Solving for x, we get x = 100.
- Therefore, in 1990, the male population is 100, and the female population is 200, making the total population 300.
Percentage Increase in Population from 1970 to 1990
- The total population in 1970 was M + F = 2M, and in 1990, the total population is 3x = 300.
- The percentage increase is (300 - 2M) / 2M * 100 = (300 - 200) / 200 * 100 = 100 / 200 * 100 = 50%.
- Therefore, the percentage increase in the total of male and female populations in the city from 1970 to 1990 is 50%.
Therefore, the correct answer is option 'B' - 68.75%.
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The total of male and female populations in a city increased by 25% fr...
Let us solve this question by assuming values(multiples of 100) and not variables(x).
Since we know that the female population was twice the male population in 1990, let us assume their respective values as 200 and 100.
Note that while assuming numbers, some of the population values might come out as a fraction(which is not possible, since the population needs to be a natural number). However, this would not affect our answer, since the calculations are in ratios and percentages and not real values of the population in any given year.
Now, we know that the female population became 1.25 times itself in 1990 from what it was in 1980.
Hence, the female population in 1980 = 200/1.25 = 160
Also, the female population became 1.2 times itself in 1980 from what it was in 1970.
Hence, the female population in 1970 = 160/1.2 = 1600/12 = 400/3
Let the male population in 1970 be x. Hence, the male population in 1980 is 1.4x.
Now, the total population in 1980 = 1.25 times the total population in 1970.
Hence, 1.25 (x + 400/3) = 1.4x + 160
Hence, x = 400/9.
Population change = 300 - 400/9 - 400/3 = 300 - 1600/9 = 1100/9
percentage change =
Since we know that the female population was twice the male population in 1990, let us assume their respective values as 200 and 100.
Note that while assuming numbers, some of the population values might come out as a fraction(which is not possible, since the population needs to be a natural number). However, this would not affect our answer, since the calculations are in ratios and percentages and not real values of the population in any given year.
Now, we know that the female population became 1.25 times itself in 1990 from what it was in 1980.
Hence, the female population in 1980 = 200/1.25 = 160
Also, the female population became 1.2 times itself in 1980 from what it was in 1970.
Hence, the female population in 1970 = 160/1.2 = 1600/12 = 400/3
Let the male population in 1970 be x. Hence, the male population in 1980 is 1.4x.
Now, the total population in 1980 = 1.25 times the total population in 1970.
Hence, 1.25 (x + 400/3) = 1.4x + 160
Hence, x = 400/9.
Population change = 300 - 400/9 - 400/3 = 300 - 1600/9 = 1100/9
percentage change =
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The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 isa)68.25b)68.75c)68.50d)69.25Correct answer is option 'B'. Can you explain this answer?
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The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 isa)68.25b)68.75c)68.50d)69.25Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 isa)68.25b)68.75c)68.50d)69.25Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 isa)68.25b)68.75c)68.50d)69.25Correct answer is option 'B'. Can you explain this answer?.
The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 isa)68.25b)68.75c)68.50d)69.25Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 isa)68.25b)68.75c)68.50d)69.25Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 isa)68.25b)68.75c)68.50d)69.25Correct answer is option 'B'. Can you explain this answer?.
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