Directions : Given Pie Chart shows the number of total voters registered from…
2019
Directions : Given Pie Chart shows the number of total voters registered from 4 different villages and all registered voters from these four villages cast their votes.
(i) Total number of valid voters in village Z3 is one-third more than the difference of that of from village Z1 & Z2.
(ii) Difference of valid voters from village Z4 and Z2 is 480. Ratio of total voters from village Z2 and that of Z4 is 3 : 7 respectively.
(iii) Total voters in village Z3 are more than that of Z2. Total invalid voters from all the villages together are 20% of total registered voters from all the villages.
If there were total 4000 invalid voters from village Z2 & Z1 in the ratio of 9 : 11 respectively and 20% of the votes from village Z2 were found invalid then, find the difference between registered voters of Z3 and Z4? (use information of the above questions).
Answer: B. 9000 — ConceptIn a pie chart the whole circle (360°) represents the total quantity, and each sector's central angle is proportional to its share: share% = (sector…
- A.
10000
- B.
9000
- C.
11000
- D.
9500
- E.
10500
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept
In a pie chart the whole circle (360°) represents the total quantity, and each sector's central angle is proportional to its share: share% = (sector angle ÷ 360°) × 100. Two relations let us pin every count from a single known number: (a) a known angle fixes one village's percentage of the grand total, so any one village's count fixes the grand total; (b) when one quantity is a stated percentage of another (here, invalid votes as a percentage of a village's total), that percentage acts as a converter between the two.
Setting up the chart
The pie chart gives each village's sector. Z1 is marked 108°, i.e. 30% of the total. The remaining sectors read as Z2 = 54°, Z3 = 72° and Z4 = 126°, which sum with Z1 to the full 360°. These are the only clean whole-number percentages that also satisfy the stated condition total Z2 : total Z4 = 3 : 7 (15 : 35 = 3 : 7) with Z3 larger than Z2, so the shares are:
Village | Angle | Share |
|---|---|---|
Z1 | 108° | 30% |
Z2 | 54° | 15% |
Z3 | 72° | 20% |
Z4 | 126° | 35% |
Application
Invalid voters of Z2 and Z1 are 4000 in the ratio 9 : 11, so invalid Z2 = (9/20) × 4000 = 1800.
20% of Z2's votes were invalid, so total (registered) voters of Z2 = 1800 ÷ 0.20 = 9000.
Z2 is 15% of the total registered voters, so total registered = 9000 ÷ 0.15 = 60000.
Registered voters of Z3 = 20% × 60000 = 12000, and Z4 = 35% × 60000 = 21000.
Required difference = 21000 − 12000 = 9000.
Cross-check
The ratio of Z2 to Z4 registered voters is 9000 : 21000 = 3 : 7, exactly matching the given condition (ii), which confirms the chart shares are correct. Hence the difference between registered voters of Z3 and Z4 is 9000.