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 are 10800 registered voters in village Z2 of which 98% votes were valid. What can be the difference between valid & invalid votes from village Z4? (use information of the above questions).
- A.
960
- B.
None of these
- C.
4992
- D.
Both (b) & (e)
- E.
3072
Show answer & explanation
Correct answer: E
Concept
In a 'valid + invalid voters' caselet, total = valid + invalid for every village, a pie sector's share of the total registered voters equals its angle / 360 degrees, and a stated total-voter ratio between two villages fixes one total once the other is known. When a difference is stated without direction ("difference of A and B is d"), it fixes only |A - B| = d and tentatively admits A = B + d and A = B - d; the remaining set conditions must then decide which sign survives, because the whole system (angles, the 20% invalid budget, and every linking condition) has to stay consistent.
Application to village Z4
Village Z2: total voters = 10800, 98% valid, so valid_Z2 = 0.98 x 10800 = 10584 and invalid_Z2 = 216.
Total-voter ratio Z2 : Z4 = 3 : 7 with Z2 = 10800 gives Z4 total = 10800 x 7/3 = 25200.
Condition (ii) fixes only the magnitude |valid_Z4 - valid_Z2| = 480, so valid_Z4 is provisionally 10584 + 480 = 11064 or 10584 - 480 = 10104.
Test both against the full system. Z1 = 108 degrees = 30% of the total registered T; total valid across all villages = 80% of T (since total invalid = 20% of T); Z3 valid = (4/3)(valid_Z1 - valid_Z2) by condition (i); and Z3 total > 10800. Solving these together, the branch valid_Z4 = 10104 leaves no value of T for which valid_Z1 stays within Z1's own total while keeping valid_Z3 non-negative under the 80% valid budget, so it is infeasible.
Only valid_Z4 = 11064 survives. Then invalid_Z4 = 25200 - 11064 = 14136, so the difference between valid and invalid votes from Z4 is |11064 - 14136| = 3072.
Cross-check
A consistent set of totals confirms it: with total registered = 72420, the angles give Z1 = 21726, Z3 = 14694, Z2 = 10800, Z4 = 25200 (sum 72420); valid_Z1 = 21600, valid_Z2 = 10584, valid_Z3 = 14688, valid_Z4 = 11064 sum to 57936 = 80% of 72420, total invalid = 14484 = 20%, condition (i) holds (4/3 x (21600 - 10584) = 14688), Z3 > Z2 holds, and valid_Z4 - valid_Z2 = 480. The valid-minus-invalid difference for Z4 is 3072. Because 4992 came only from the infeasible minus branch, it is a distractor, 'both values' is wrong since only one survives, and 960 never matches any consistent Z4 split.