Pie chart (i) shows the percentage distribution of the total people (male +…
2023
Pie chart (i) shows the percentage distribution of the total people (male + female) who visited five different clubs, and pie chart (ii) shows the percentage distribution of the total males who visited these five clubs. Study the data carefully and answer the question given below.
If the total females who visited club F are 25% more than the total females who visited club E, and the total number of people who visited club F is 11/8 of the total number of males who visited club D, then find the ratio of the total males who visited club F to the total males who visited club E.
- A.
29 : 72
- B.
31 : 72
- C.
37 : 72
- D.
23 : 72
- E.
25 : 72
Show answer & explanation
Correct answer: B
Concept
In a two-pie data set, one pie gives the percentage split of a total (here total people = 2500) and the other gives the split of a sub-group (here total males = 1200). The number for any category is found by taking its percentage of the matching grand total. The count of one gender in a club is the difference: Females = Total people in that club minus Males in that club. Read each value from the pie that owns it, then combine.
Working
Read the totals and the needed slices. Total people = 2500; total males = 1200. From pie (i): club E = 12% of people. From pie (ii): club E males = 18%, club D males = 12% of males.
Females in club E = (people in E) - (males in E) = (12% of 2500) - (18% of 1200) = 300 - 216 = 84.
Females in club F = 25% more than females in E = 84 x 1.25 = 105.
Males in club D = 12% of 1200 = 144. Total people in club F = (11/8) of males in D = (11/8) x 144 = 198.
Males in club F = total people in F - females in F = 198 - 105 = 93. Males in club E = 18% of 1200 = 216.
Required ratio = males in F : males in E = 93 : 216. Divide both by their HCF, 3: 93/3 = 31 and 216/3 = 72, giving 31 : 72.
Cross-check
Reverse the ratio: 31 : 72 scaled by 3 gives 93 : 216, and 93 + 105 = 198 = (11/8) x 144 confirms the club F total, while 216 = 18% of 1200 confirms males in E. All conditions hold, so the ratio is 31 : 72.