The following table shows the percentage (%) distribution of number of members…
2023
The following table shows the percentage (%) distribution of number of members (both male and female) and number of male members in five health clubs A-E in the year 2022. Total number of members (both male and female) in health club C is 1764 and number of male members in health club E is 576. Based on the data in the table, answer the questions that follow
Health Club-Wise Distribution of Members
Health Club | Members (Male & Female) | Male |
|---|---|---|
A | 21% | 21% |
B | 33% | 32% |
C | 14% | 19% |
D | 20% | 20% |
E | 12% | 8% |
Number of female members in health club E is ____% less than the number of male members in health club B.
Answer: B. \(59\frac{3}{8}\%\) — ConceptWhen a category accounts for p% of a known grand total, its count is (p/100) × grand total. Conversely, grand total = category count ÷ (p/100). If X is…
- A.
\(56\frac{2}{3}\%\)
- B.
\(59\frac{3}{8}\%\)
- C.
\(54\frac{1}{2}\%\)
- D.
\(60\frac{2}{3}\%\)
Show answer & explanation
Correct answer: B
Concept
When a category accounts for p% of a known grand total, its count is (p/100) × grand total. Conversely, grand total = category count ÷ (p/100).
If X is less than Y, the percentage decrease is ((Y − X)/Y) × 100.
Application
Since club C has 1,764 members and represents 14% of all members, the total number of members is 1,764 ÷ 0.14 = 12,600.
Club E therefore has 12% of 12,600 = 1,512 members. Its female membership is 1,512 − 576 = 936.
Since 576 male members in club E represent 8% of all male members, the total number of male members is 576 ÷ 0.08 = 7,200.
Male members in club B = 32% of 7,200 = 2,304.
Required percentage decrease = ((2,304 − 936)/2,304) × 100 = (1,368/2,304) × 100 = 59.375% = \(59\frac{3}{8}\%\).
Cross-check
40.625% of 2,304 is 936, so 936 is 59.375% less than 2,304.
Therefore, the required percentage is \(59\frac{3}{8}\%\).