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 |
If the population of males below poverty line for state ‘B’ is 2.4 million and that for state ‘E’ is 6 million, the total population of states ‘B’ and ‘E’ is in the ratio of _____.
Answer: A. 2 : 5 — ConceptA subgroup’s share of a total equals the group percentage multiplied by that subgroup’s fraction within the group. When two totals have the same…
- A.
2 : 5
- B.
2 : 7
- C.
3 : 7
- D.
4 : 9
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
A subgroup’s share of a total equals the group percentage multiplied by that subgroup’s fraction within the group.
When two totals have the same subgroup share, the ratio of the totals equals the ratio of the corresponding subgroup counts.
Application
For state B, the male-below-poverty share is 25% × 3/(3 + 5) = 25% × 3/8 = 3/32 of B’s total population.
Therefore, B’s total population is 2.4 × 32/3 = 25.6 million.
For state E, the male-below-poverty share is 15% × 5/(5 + 3) = 15% × 5/8 = 3/32 of E’s total population.
Therefore, E’s total population is 6 × 32/3 = 64 million.
Thus, B : E = 25.6 : 64 = 2 : 5.
Cross-check
Both states have exactly 3/32 of their total population in the stated male-below-poverty subgroup. Hence 25.6 × 3/32 = 2.4 million and 64 × 3/32 = 6 million, matching the data.
The required ratio is 2 : 5.