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Question

Based on the data in table, answer the five questions that follow:

The following table shows the break‐up of population in terms of males, females and transgenders of five different cities A ‐ E. Some of the data in the table is in percent (%) while some data is in numbers.

City‐wise Break‐up of Population

CityPopulation Break-up
MalesFemalesTransgenders
A45%30%2000
B50%300035%
C800035%15%
D45%360025%
E38%32%4200

Population of City 'C' is what percent less than the population of City 'B'?

The correct answer is

20%

The question asks us to find the percentage difference between the population of City 'C' and City 'B' based on the provided data table. To do this, we first need to calculate the total population for both City 'C' and City 'B' using the given percentages and numbers.

City Population Break-up Males Females Transgenders
A 45% 30% 2000
B   50% 3000 35%
C   8000 35% 15%
D   45% 3600 25%
E   38% 32% 4200

Calculating Population of City C

In City C, we are given the number of males and the percentages of females and transgenders.

  • Number of Males = 8000
  • Percentage of Females = 35%
  • Percentage of Transgenders = 15%

The total percentage of Females and Transgenders in City C is:

\( \text{Percentage of Females + Percentage of Transgenders} = 35\% + 15\% = 50\% \)

This means the remaining population, which are the males, constitute the rest of the percentage:

\( \text{Percentage of Males} = 100\% - 50\% = 50\% \)

So, 50% of the total population of City C is equal to 8000. We can use this to find the total population of City C.

Let the total population of City C be \(P_C\). Then:

\( 50\% \text{ of } P_C = 8000 \)

\( 0.50 \times P_C = 8000 \)

\( P_C = \frac{8000}{0.50} \)

\( P_C = 16000 \)

The total population of City C is 16000.

Calculating Population of City B

In City B, we are given the number of females and the percentages of males and transgenders.

  • Percentage of Males = 50%
  • Number of Females = 3000
  • Percentage of Transgenders = 35%

The total percentage of Males and Transgenders in City B is:

\( \text{Percentage of Males + Percentage of Transgenders} = 50\% + 35\% = 85\% \)

This means the remaining population, which are the females, constitute the rest of the percentage:

\( \text{Percentage of Females} = 100\% - 85\% = 15\% \)

So, 15% of the total population of City B is equal to 3000. We can use this to find the total population of City B.

Let the total population of City B be \(P_B\). Then:

\( 15\% \text{ of } P_B = 3000 \)

\( 0.15 \times P_B = 3000 \)

\( P_B = \frac{3000}{0.15} \)

\( P_B = 20000 \)

The total population of City B is 20000.

Calculating Percentage Less

Now we need to find out what percentage less is the population of City C compared to the population of City B. The formula for percentage less is:

\( \text{Percentage Less} = \frac{\text{Value 1} - \text{Value 2}}{\text{Value 1}} \times 100 \)

In this case, Value 1 is the population of City B (20000) and Value 2 is the population of City C (16000).

Difference in population = Population of City B - Population of City C

\( \text{Difference} = 20000 - 16000 = 4000 \)

Now, calculate the percentage less:

\( \text{Percentage Less} = \frac{\text{Difference}}{\text{Population of City B}} \times 100 \)

\( \text{Percentage Less} = \frac{4000}{20000} \times 100 \)

\( \text{Percentage Less} = \frac{4}{20} \times 100 \)

\( \text{Percentage Less} = \frac{1}{5} \times 100 \)

\( \text{Percentage Less} = 0.20 \times 100 \)

\( \text{Percentage Less} = 20\% \)

The population of City C is 20% less than the population of City B.

Revision Table: Key Data and Calculations

City Given Data Used Calculation for Total Population Total Population
C Males: 8000
Females: 35%, Transgenders: 15%
50% = 8000
\(P_C = 8000 / 0.50\)
16000
B Females: 3000
Males: 50%, Transgenders: 35%
15% = 3000
\(P_B = 3000 / 0.15\)
20000
Comparison C vs B \(P_C = 16000\)
\(P_B = 20000\)
\(\frac{P_B - P_C}{P_B} \times 100 = \frac{20000-16000}{20000} \times 100\) 20% less

Additional Information: Data Interpretation Concepts

Data interpretation questions often involve tables, charts, and graphs that require careful reading and calculation. Key concepts used here include:

  • Percentage Calculation: Understanding how to find a part of a whole or the whole when a part and its percentage are known. The formula \( \text{Part} = \frac{\text{Percentage}}{100} \times \text{Whole} \) and rearrangements are fundamental.
  • Percentage Difference/Change: Calculating how much a value has changed relative to an original value. The formula for percentage less is \( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100 \).
  • Analyzing Table Data: Extracting relevant information from rows and columns and understanding the units (numbers or percentages).

These skills are crucial for solving quantitative aptitude problems based on data sets like this population break-up table.

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Important Questions from Tabulation

  1. The table shows District-wise data of a number of primary school teachers posted in schools of a city.

    Study the table and answer the question:

    District

    Male teachers

    Female teachers

    East

    1650

    2375

    North

    1075

    2651

    West

    1280

    1520

    South

    1170

    1085

    Central

    690

    859


    What is the difference between the total number of male teachers in the districts East, North, West taken together and the total number of female teachers in the districts East and South?
  2. Table shows income (in Rs. ) received by 4 employees of a company during the month of December 2020 and all their income sources.

    Source

    Amit

    Suresh

    Nitin

    Varun

    Salary

    35000

    38500

    29000

    42000

    Arrears

    6000

    6300

    5000

    7500

    Bonus

    1000

    1100

    1000

    1240

    Overtime

    1800

    1950

    1400

    1500


    What is the ratio of salary of Varun to his income other than salary?
  3. Study the table and answer the question:

    Income (Rs.)

    No. of persons

    Less than 200

    12

    Less than 250

    26

    Less than 300

    34

    Less than 350

    40

    Less than 400

    50


    What is the percentage of persons earning Rs. 250 or more?
  4. The following table shows the annual profit of a company (in Rs. lakh).

    2014-2015

    2015-2016

    2016-0217

    2017-2018

    2018-2019

    625

    690

    725

    775

    815

    The period which has the maximum percentage increase in profit over the previous year is:

  5. The table given below shows the number of persons participating in a survey from 6 different states.

    States Persons 
    S1100
    S2200 
    S3400 
    S4500 
    S5600 
    S6800

    What is the ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4?

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