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09 Jul 2024, 05:17
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Solution-
Number of female voters in the year 2000 --> 3300R because R represents the ratio of female to male voters in the year 2000. Given the number of male voters were 3300 so multipying 3300 with R will give the actual total number of female voters in the year 2000.
The Ratio of female to male voters in the year 2020-->
F is positive (Percent Increase) and M is negative (Percent Decrease). Thus (100+F) will represent the percent change of female voters from 2000 and (100-M) represents the percent chage of male voters from 2000.
Thus R*(100+F)/(100-M) will give the ratio of female to male voters in the year 2020 as the initial ratio was R in 2000.
Thus final answer will be-
Number of female voters in the year 2000 --> 3300R
The Ratio of female to male voters in the year 2020-->R*(100+F)/(100-M)
Number of female voters in the year 2000 --> 3300R because R represents the ratio of female to male voters in the year 2000. Given the number of male voters were 3300 so multipying 3300 with R will give the actual total number of female voters in the year 2000.
The Ratio of female to male voters in the year 2020-->
F is positive (Percent Increase) and M is negative (Percent Decrease). Thus (100+F) will represent the percent change of female voters from 2000 and (100-M) represents the percent chage of male voters from 2000.
Thus R*(100+F)/(100-M) will give the ratio of female to male voters in the year 2020 as the initial ratio was R in 2000.
Thus final answer will be-
Number of female voters in the year 2000 --> 3300R
The Ratio of female to male voters in the year 2020-->R*(100+F)/(100-M)
09 Jul 2024, 05:39
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#### Solution By Steps
***Step 1: Identify the given information***
- Elections were held every 5 years from 2000 to 2020.
- Number of male voters decreased from 3300 in 2000.
- F and M represent the percentage change in female and male voters, respectively.
- R represents the ratio of female to male voters in 2000.
***Step 2: Define the variables***
- Let \( N_{F2000} \) be the number of female voters in 2000.
- Let \( N_{M2000} \) be the number of male voters in 2000, which is 3300.
***Step 3: Calculate the number of female voters in 2000***
- Since \( N_{M2000} = 3300 \), and R is the ratio of female to male voters in 2000, we have:
\[
N_{F2000} = R \times 3300
\]
***Step 4: Calculate the number of female and male voters in 2020***
- The percentage change in female voters is F, so the number of female voters in 2020 is:
\[
N_{F2020} = N_{F2000} \times (1 + \frac{F}{100})
\]
- The percentage change in male voters is M, so the number of male voters in 2020 is:
\[
N_{M2020} = 3300 \times (1 - \frac{M}{100})
\]
***Step 5: Calculate the ratio of female to male voters in 2020***
- The ratio of female to male voters in 2020 is:
\[
R_{2020} = \frac{N_{F2020}}{N_{M2020}} = \frac{N_{F2000} \times (1 + \frac{F}{100})}{3300 \times (1 - \frac{M}{100})}
\]
- Substituting \( N_{F2000} = R \times 3300 \):
\[
R_{2020} = \frac{R \times 3300 \times (1 + \frac{F}{100})}{3300 \times (1 - \frac{M}{100})} = \frac{R \times (1 + \frac{F}{100})}{(1 - \frac{M}{100})}
\]
#### Final Answer
- The number of female voters in 2000 is \( R \times 3300 \).
- The ratio of female to male voters in 2020 is \( \frac{R \times (1 + \frac{F}{100})}{(1 - \frac{M}{100})} \).
***Step 1: Identify the given information***
- Elections were held every 5 years from 2000 to 2020.
- Number of male voters decreased from 3300 in 2000.
- F and M represent the percentage change in female and male voters, respectively.
- R represents the ratio of female to male voters in 2000.
***Step 2: Define the variables***
- Let \( N_{F2000} \) be the number of female voters in 2000.
- Let \( N_{M2000} \) be the number of male voters in 2000, which is 3300.
***Step 3: Calculate the number of female voters in 2000***
- Since \( N_{M2000} = 3300 \), and R is the ratio of female to male voters in 2000, we have:
\[
N_{F2000} = R \times 3300
\]
***Step 4: Calculate the number of female and male voters in 2020***
- The percentage change in female voters is F, so the number of female voters in 2020 is:
\[
N_{F2020} = N_{F2000} \times (1 + \frac{F}{100})
\]
- The percentage change in male voters is M, so the number of male voters in 2020 is:
\[
N_{M2020} = 3300 \times (1 - \frac{M}{100})
\]
***Step 5: Calculate the ratio of female to male voters in 2020***
- The ratio of female to male voters in 2020 is:
\[
R_{2020} = \frac{N_{F2020}}{N_{M2020}} = \frac{N_{F2000} \times (1 + \frac{F}{100})}{3300 \times (1 - \frac{M}{100})}
\]
- Substituting \( N_{F2000} = R \times 3300 \):
\[
R_{2020} = \frac{R \times 3300 \times (1 + \frac{F}{100})}{3300 \times (1 - \frac{M}{100})} = \frac{R \times (1 + \frac{F}{100})}{(1 - \frac{M}{100})}
\]
#### Final Answer
- The number of female voters in 2000 is \( R \times 3300 \).
- The ratio of female to male voters in 2020 is \( \frac{R \times (1 + \frac{F}{100})}{(1 - \frac{M}{100})} \).
RenB
Joined: 13 Jul 2022
Last visit: 02 Mar 2026
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Location: India
Concentration: Finance, Nonprofit
Schools: Stanford '26 Wharton '26 (D) Booth '26 (D) Yale '26 (D) CBS '26 (A$$$) Darden '26 (WL) HBS '26 (D) Ross '26 (A$$$$) LBS '26 (D) Tuck '26 (A$$) Kellogg '26 (A)
GMAT Focus 1: 715 Q90 V84 DI82 
GPA: 3.74
WE:Corporate Finance (Consulting)
Schools: Stanford '26 Wharton '26 (D) Booth '26 (D) Yale '26 (D) CBS '26 (A$$$) Darden '26 (WL) HBS '26 (D) Ross '26 (A$$$$) LBS '26 (D) Tuck '26 (A$$) Kellogg '26 (A)
GMAT Focus 1: 715 Q90 V84 DI82
Posts: 389
Kudos:
1,467
09 Jul 2024, 06:00
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Bunuel
Attaching my working
