The pie chart (i) given below shows the percentage distribution of total…
2023
The pie chart
(i) given below shows the percentage distribution of total people (male + female) who visited five different clubs, and pie chart
(ii) shows the percentage distribution of total males who visited these five clubs. Read the data carefully and answer the question given below.
In club C, the ratio of males aged above 25 years to males aged below 25 years is 5 : 3, while in club B the ratio of females aged above 25 years to females aged below 25 years is 1 : 2. If the number of males in C and the number of females in B who are exactly 25 years old are 20 and 40 respectively, then find the sum of the total males in C and the total females in B who are aged below 25 years.
- A.
300
- B.
320
- C.
270
- D.
250
- E.
210
Show answer & explanation
Correct answer: C
Concept
In a pie-chart data-interpretation problem, the count for any sector equals its percentage multiplied by the relevant grand total. When a group is then split into sub-parts in a ratio a : b after setting aside a fixed "exactly equal" carve-out, first subtract that carve-out from the group, then divide the remainder in the given ratio: each ratio-part = (group total − carve-out) / (a + b).
Application
Total people = 2500. Males in club C = 35% of total males = 0.35 × 1200 = 420.
Total people in club B = 16% of 2500 = 400; males in club B = 15% of 1200 = 180; so females in B = 400 − 180 = 220.
Club C males split (above : below 25) = 5 : 3 after removing the 20 who are exactly 25: remaining = 420 − 20 = 400, so one part = 400 / (5 + 3) = 50; males below 25 in C = 3 × 50 = 150.
Club B females split (above : below 25) = 1 : 2 after removing the 40 who are exactly 25: remaining = 220 − 40 = 180, so one part = 180 / (1 + 2) = 60; females below 25 in B = 2 × 60 = 120.
Required sum = males below 25 in C + females below 25 in B = 150 + 120 = 270.
Cross-check
Reconcile each group: club C males = 250 (above 25) + 150 (below 25) + 20 (exactly 25) = 420, which matches 35% of 1200. Club B females = 60 (above 25) + 120 (below 25) + 40 (exactly 25) = 220, which matches 400 − 180. Both groups balance, so the required sum 270 is consistent.