Consider the following table that embodies details about the percentage…
2022
Consider the following table that embodies details about the percentage distribution of population of five states A-E on the basis of poverty line and gender. In accordance with the data in the table, answer the questions 1-5:
State-wise Distribution of Population
State | Percentage (%) of Population Below Poverty Line | Below Poverty Line — M : F | Above Poverty Line — M : F |
|---|---|---|---|
A | 35 | 5 : 6 | 6 : 7 |
B | 25 | 3 : 5 | 4 : 5 |
C | 24 | 1 : 2 | 2 : 3 |
D | 19 | 3 : 2 | 5 : 3 |
E | 15 | 5 : 3 | 3 : 2 |
What will be the number of females above poverty line in the state ‘D’, if it is known that the population of the state ‘D’ is 8 million?
Answer: D. 2.43 million — ConceptFor a population split by a percentage and then by a ratio, first isolate the required percentage group. Next, convert the relevant gender ratio into…
- A.
3 million
- B.
2.83 million
- C.
2.63 million
- D.
2.43 million
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept
For a population split by a percentage and then by a ratio, first isolate the required percentage group. Next, convert the relevant gender ratio into that gender’s fraction of the group.
If p% is below the poverty line, the above-poverty population is T × (100 − p)/100. For a male-to-female ratio m:f, the female share is f/(m + f).
Application
For state D, 19% is below the poverty line, so 100% − 19% = 81% is above it.
The above-poverty population is 8 × 81/100 = 6.48 million.
The male-to-female ratio above the poverty line is 5:3, so females form 3/(5 + 3) = 3/8 of that group.
Therefore, the number of females above the poverty line is 6.48 × 3/8 = 2.43 million.
Cross-check
The corresponding male population is 6.48 × 5/8 = 4.05 million. Their total is 4.05 + 2.43 = 6.48 million, and 4.05:2.43 simplifies to 5:3, matching the table.
Thus, the required number of females is 2.43 million.