Directions (1 - 2): The table shows the percentage of total population of a…
2024
Directions (1 - 2): The table shows the percentage of total population of a city in different age groups. Study the table and answer the questions.
Age Group | Percent |
|---|---|
Up to 15 | 20.00 |
16 - 25 | 18.25 |
26 - 35 | 16.75 |
36 - 45 | 16.25 |
46 - 55 | 15.00 |
56 - 65 | 12.50 |
66 and above | 1.25 |
If the difference between the number of people in the age groups (46 -55) and (16 - 25) is 0.975 million, then the total population (in millions) of the city is:
Answer: B. 30 million — Concept: When the values of two known percentages of a total are given, along with the actual (absolute) difference between the quantities each percentage…
- A.
27 million
- B.
30 million
- C.
22 million
- D.
25 million
Attempted by 4 students.
Show answer & explanation
Correct answer: B
Concept: When the values of two known percentages of a total are given, along with the actual (absolute) difference between the quantities each percentage represents, the total can be found by treating the percentage-point difference as the same fraction of the total as the absolute difference: (percentage-point difference)% of Total = given absolute difference, so Total = (absolute difference ÷ percentage-point difference) × 100.
Working:
From the table, the percentage for age group 16-25 is 18.25% and for age group 46-55 is 15.00%.
The percentage-point difference between these two rows = 18.25% − 15.00% = 3.25%.
This 3.25% of the total population corresponds to the given absolute difference of 0.975 million people, so 3.25% of Total = 0.975 million.
Therefore 1% of Total = 0.975 ÷ 3.25 = 0.3 million.
Scaling up to 100%, Total = 0.3 × 100 = 30 million.
Check: 3.25% of 30 million = (3.25/100) × 30 = 0.975 million, which matches the difference given in the question — confirming the total population is 30 million.