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Three persons ran for office and got 1136, 7636, and 11628 votes, respectively. What was the winning candidate's percentage of the total votes?
तीन व्यक्तियों ने चुनाव लड़ा और उन्हें क्रमशः 1136, 7636 और 11628 मत प्राप्त हुए। जीतने वाले उम्मीदवार को कुल मतों का कितना प्रतिशत प्राप्त हुआ?
(A) (a) 57%
(B) (b) 59%
(C) (c) 52%
(D) (d) 61%
✅ Answer & Explanation
Sahi jawab: A) (a) 57%Explanation: Method 1 (Direct Percentage Method): Total votes polled = 1136 + 7636 + 11628 = 20400. Winning candidate got maximum votes = 11628. Winning percentage = \frac{11628}{20400} \times 100% = \frac{11628}{204}% = 57%. Atah sahi vikalp (a) 57% hai. Method 2 (Unit Digit / Divisibility Method): \frac{11628}{204} = \frac{2907}{51} = 57%. Since 204 \times 50 = 10200 and 204 \times 7 = 1428, 10200 + 1428 = 11628. Atah sahi uttar (a) hai.
The difference between 31% and 26% of votes for the same party at different places is 2350. What is 7% of those votes?
अलग-अलग स्थानों पर एक ही पार्टी के लिए 31% और 26% मतों के बीच का अंतर 2350 है। उन मतों का 7% कितना है?
(A) (a) 2270
(B) (b) 3090
(C) (c) 4090
(D) (d) 3290
✅ Answer & Explanation
Sahi jawab: D) (d) 3290Explanation: Method 1 (Percentage Difference Method): Difference in percentage = 31% - 26% = 5%. Given: 5% = 2350. 1% = \frac{2350}{5} = 470. Value of 7% = 7 \times 470 = 3290. Atah sahi vikalp (d) 3290 hai. Method 2 (Unitary Ratio Method): Required value = 2350 \times \frac{7}{5} = 470 \times 7 = 3290. Atah sahi uttar (d) hai.
Two candidates contested an election. One of them got 64% of the votes and won by 434 votes. What was the total number of votes polled?
दो उम्मीदवारों ने एक चुनाव लड़ा। उनमें से एक को 64% मत मिले और वह 434 मतों से जीत गया। कुल डाले गए मतों की संख्या क्या थी?
(A) (a) 1550
(B) (b) 1345
(C) (c) 1680
(D) (d) 1684
✅ Answer & Explanation
Sahi jawab: A) (a) 1550Explanation: Method 1 (100-Base Method): Total votes = 100%. Winner got = 64% ==> Loser got = 100% - 64% = 36%. Winning majority margin = 64% - 36% = 28%. Given: 28% = 434. 1% = \frac{434}{28} = 15.5. Total votes (100%) = 15.5 \times 100 = 1550. Atah sahi vikalp (a) 1550 hai. Method 2 (Ratio Method): Winner : Loser = 64 : 36 = 16 : 9. Total = 25 units. Margin = 16 - 9 = 7 units. 7 units = 434 ==> 1 unit = 62. Total votes = 25 units = 25 \times 62 = 1550. Atah sahi uttar (a) hai.
In an election between two candidates, the one who gets 88% of the votes is elected by a majority of 684 votes. What is the total number of votes polled? (all polled votes are valid)
दो उम्मीदवारों के बीच एक चुनाव में, 88% मत प्राप्त करने वाला उम्मीदवार 684 मतों के बहुमत से चुना जाता है। डाले गए मतों की कुल संख्या क्या है? (सभी डाले गए मत वैध हैं)
(A) (a) 900
(B) (b) 800
(C) (c) 850
(D) (d) 750
✅ Answer & Explanation
Sahi jawab: A) (a) 900Explanation: Method 1 (100-Base Method): Winner = 88%, Loser = 100% - 88% = 12%. Majority margin = 88% - 12% = 76%. Given: 76% = 684. 1% = \frac{684}{76} = 9. Total votes (100%) = 9 \times 100 = 900. Atah sahi vikalp (a) 900 hai. Method 2 (Ratio Method): Winner : Loser = 88 : 12 = 22 : 3. Total = 25 units. Difference = 22 - 3 = 19 units. 19 units = 684 ==> 1 unit = 36. Total votes = 25 \times 36 = 900. Atah sahi uttar (a) hai.
In an election, a candidate secured 41% of the votes polled and lost the election by 97,632. What is the number of votes obtained by the winning candidate?
एक चुनाव में, एक उम्मीदवार ने डाले गए मतों का 41% प्राप्त किया और वह 97,632 मतों से चुनाव हार गया। जीतने वाले उम्मीदवार द्वारा प्राप्त मतों की संख्या क्या है?
(A) (a) 320016
(B) (b) 542400
(C) (c) 222384
(D) (d) 360072
✅ Answer & Explanation
Sahi jawab: A) (a) 320016Explanation: Method 1 (100-Base Method): Loser = 41% ==> Winner = 100% - 41% = 59%. Margin = 59% - 41% = 18%. Given: 18% = 97632. 1% = \frac{97632}{18} = 5424. Winning candidate got 59% = 59 \times 5424 = 320016. Atah sahi vikalp (a) 320016 hai. Method 2 (Direct Ratio Fraction Method): Winner's votes = 97632 \times \frac{59}{18} = 5424 \times 59 = 320016. Atah sahi uttar (a) hai.
In an election between two candidates A and B, A got 33% of total votes casted and still lost by 55,522 votes. Find the total number of votes got by B.
दो उम्मीदवारों A और B के बीच एक चुनाव में, A को डाले गए कुल मतों का 33% मिला और फिर भी वह 55,522 मतों से हार गया। B द्वारा प्राप्त कुल मतों की संख्या ज्ञात कीजिए।
(A) (a) 1,09,411
(B) (b) 1,09,511
(C) (c) 1,09,311
(D) (d) 1,08,411
✅ Answer & Explanation
Sahi jawab: A) (a) 1,09,411Explanation: Method 1 (100-Base Method): A = 33% ==> B = 100% - 33% = 67%. Margin between B and A = 67% - 33% = 34%. Given: 34% = 55522. 1% = \frac{55522}{34} = 1633. Votes got by B (67%) = 67 \times 1633 = 109411. Atah sahi vikalp (a) 1,09,411 hai. Method 2 (Ratio Formulation): B's votes = 55522 \times \frac{67}{34} = 1633 \times 67 = 109411. Atah sahi uttar (a) hai.
In an election there were only two candidates. One of the candidates secured 35% of votes and is defeated by the other candidate by 381 votes. The total number of votes polled is:
एक चुनाव में केवल दो उम्मीदवार थे। उम्मीदवारों में से एक ने 35% मत प्राप्त किए और वह दूसरे उम्मीदवार से 381 मतों से पराजित हो गया। डाले गए कुल मतों की संख्या है:
(A) (a) 1270
(B) (b) 1028
(C) (c) 635
(D) (d) 514
✅ Answer & Explanation
Sahi jawab: A) (a) 1270Explanation: Method 1 (100-Base Method): Total votes polled = 100%. Defeated candidate = 35%. Winning candidate = 100% - 35% = 65%. Defeat margin = 65% - 35% = 30%. Given: 30% = 381. 1% = \frac{381}{30} = 12.7. Total votes (100%) = 12.7 \times 100 = 1270. Atah sahi vikalp (a) 1270 hai. Method 2 (Ratio Method): Ratio of votes (Winner : Loser) = 65 : 35 = 13 : 7. Total votes = 13 + 7 = 20 units. Margin = 13 - 7 = 6 units. 6 units = 381 ==> 1 unit = 63.5. Total votes = 20 \times 63.5 = 1270. Atah sahi uttar (a) hai.
In an election, a candidate secures 40% of the votes, but is defeated by the only other candidate with a majority of 298 votes. Find the total number of votes recorded.
एक चुनाव में, एक उम्मीदवार 40% मत प्राप्त करता है, लेकिन एकमात्र अन्य उम्मीदवार से 298 मतों के बहुमत से पराजित हो जाता है। डाले गए कुल मतों की संख्या ज्ञात कीजिए।
(A) (a) 1,470
(B) (b) 1,490
(C) (c) 1,270
(D) (d) 1,290
✅ Answer & Explanation
Sahi jawab: B) (b) 1,490Explanation: Method 1 (100-Base Method): Total votes = 100%. Candidate 1 (Loser) = 40%. Candidate 2 (Winner) = 100% - 40% = 60%. Margin = 60% - 40% = 20%. Given: 20% = 298. Multiply both sides by 5 to get 100%: Total votes (100%) = 298 \times 5 = 1490. Atah sahi vikalp (b) 1,490 hai. Method 2 (Ratio Method): Winner : Loser = 60 : 40 = 3 : 2. Total = 5 units. Difference = 3 - 2 = 1 unit. 1 unit = 298. Total votes recorded = 5 \times 298 = 1490. Atah sahi uttar (b) hai.
In an election, there were only two candidates. One of the candidates secured 44% of the votes and is defeated by the other candidate by 1440 votes. If there were no invalid votes, then the total number of votes polled is:
एक चुनाव में केवल दो उम्मीदवार थे। उम्मीदवारों में से एक ने 44% मत प्राप्त किए और वह दूसरे उम्मीदवार से 1440 मतों से हार गया। यदि कोई अमान्य मत नहीं था, तो डाले गए मतों की कुल संख्या है:
(A) (a) 14000
(B) (b) 12000
(C) (c) 15000
(D) (d) 13000
✅ Answer & Explanation
Sahi jawab: B) (b) 12000Explanation: Method 1 (100-Base Method): Total votes = 100%. Loser = 44% ==> Winner = 100% - 44% = 56%. Defeat margin = 56% - 44% = 12%. Given: 12% = 1440. 1% = \frac{1440}{12} = 120. Total votes polled (100%) = 120 \times 100 = 12000. Atah sahi vikalp (b) 12000 hai. Method 2 (Ratio Method): Winner : Loser = 56 : 44 = 14 : 11. Difference = 14 - 11 = 3 units. 3 units = 1440 ==> 1 unit = 480. Total votes = (14 + 11) \times 480 = 25 \times 480 = 12000. Atah sahi uttar (b) hai.
In an election a candidate secured 47% of the votes and lost to his only opponent by 276 votes. Find the total number of votes polled.
एक चुनाव में एक उम्मीदवार ने 47% मत प्राप्त किए और वह अपने एकमात्र प्रतिद्वंद्वी से 276 मतों से हार गया। डाले गए कुल मतों की संख्या ज्ञात कीजिए।
(A) (a) 4000
(B) (b) 4200
(C) (c) 3800
(D) (d) 4600
✅ Answer & Explanation
Sahi jawab: D) (d) 4600Explanation: Method 1 (100-Base Method): Total votes = 100%. Loser = 47% ==> Winner = 100% - 47% = 53%. Difference = 53% - 47% = 6%. Given: 6% = 276. 1% = \frac{276}{6} = 46. Total votes polled (100%) = 46 \times 100 = 4600. Atah sahi vikalp (d) 4600 hai. Method 2 (Ratio Method): Winner : Loser = 53 : 47. Margin = 53 - 47 = 6 units. 6 units = 276 ==> 1 unit = 46. Total votes = (53 + 47) \times 46 = 100 \times 46 = 4600. Atah sahi uttar (d) hai.
In an election there were three candidates. The first candidate got 40% votes and second candidate got 35% votes. If the total votes in the election are 50,000, find the number of votes got by the third candidate.
एक चुनाव में तीन उम्मीदवार थे। पहले उम्मीदवार को 40% मत और दूसरे उम्मीदवार को 35% मत मिले। यदि चुनाव में कुल मत 50,000 हैं, तो तीसरे उम्मीदवार को मिले मतों की संख्या ज्ञात कीजिए।
(A) (a) 12,000
(B) (b) 12,500
(C) (c) 13,000
(D) (d) 15,000
✅ Answer & Explanation
Sahi jawab: B) (b) 12,500Explanation: Method 1 (100-Base Method): Total votes = 100% = 50,000. First candidate = 40%. Second candidate = 35%. Third candidate = 100% - (40% + 35%) = 100% - 75% = 25%. Votes for 3rd candidate = 25% of 50000 = \frac{25}{100} \times 50000 = 12500. Atah sahi vikalp (b) 12,500 hai. Method 2 (Ratio Method): Ratio of Candidates (1st : 2nd : 3rd) = 40 : 35 : 25 = 8 : 7 : 5. Total units = 8 + 7 + 5 = 20 units. 20 units = 50000 ==> 1 unit = 2500. Third candidate = 5 units = 5 \times 2500 = 12500. Atah sahi uttar (b) hai.
In an election between two candidates, one candidate gets 72% of the total votes cast. If the total votes are 1000, by how many votes does the winner win the election?
दो उम्मीदवारों के बीच एक चुनाव में, एक उम्मीदवार को डाले गए कुल मतों का 72% प्राप्त होता है। यदि कुल मत 1000 हैं, तो जीतने वाला उम्मीदवार कितने मतों से चुनाव जीतता है?
(A) (a) 360
(B) (b) 250
(C) (c) 720
(D) (d) 440
✅ Answer & Explanation
Sahi jawab: D) (d) 440Explanation: Method 1 (100-Base Method): Total votes = 100% = 1000. Winner got = 72%. Loser got = 100% - 72% = 28%. Winning margin = 72% - 28% = 44%. Number of votes by which winner wins = 44% of 1000 = \frac{44}{100} \times 1000 = 440. Atah sahi vikalp (d) 440 hai. Method 2 (Ratio Method): Winner : Loser = 72 : 28 = 18 : 7. Total units = 18 + 7 = 25 units. Given: 25 units = 1000 ==> 1 unit = \frac{1000}{25} = 40. Winning margin = 18 - 7 = 11 units. Margin in votes = 11 \times 40 = 440. Atah sahi uttar (d) hai.
In an election between two candidates, a candidate who gets 78% of the votes is elected by a majority of 448 votes. What is the total number of votes polled?
दो उम्मीदवारों के बीच एक चुनाव में, 78% मत प्राप्त करने वाला उम्मीदवार 448 मतों के बहुमत से निर्वाचित होता है। डाले गए मतों की कुल संख्या क्या है?
(A) (a) 800
(B) (b) 900
(C) (c) 750
(D) (d) 850
✅ Answer & Explanation
Sahi jawab: A) (a) 800Explanation: Method 1 (100-Base Method): Total votes polled = 100%. Winning candidate = 78%. Losing candidate = 100% - 78% = 22%. Winning majority margin = 78% - 22% = 56%. Given: 56% = 448. 1% = \frac{448}{56} = 8. Total number of votes polled (100%) = 8 \times 100 = 800. Atah sahi vikalp (a) 800 hai. Method 2 (Ratio Method): Winner : Loser = 78 : 22 = 39 : 11. Total units = 39 + 11 = 50 units. Difference between them = 39 - 11 = 28 units. Given: 28 units = 448 ==> 1 unit = \frac{448}{28} = 16. Total votes polled = 50 units = 50 \times 16 = 800. Atah sahi uttar (a) hai.
In an election between two candidates, the candidate who gets 35% of the votes polled is defeated by 15,900 votes. What is the total number of votes polled?
दो उम्मीदवारों के बीच एक चुनाव में, डाले गए मतों का 35% मत प्राप्त करने वाला उम्मीदवार 15,900 मतों से पराजित हो जाता है। डाले गए मतों की कुल संख्या क्या है?
(A) (a) 53,000
(B) (b) 45,000
(C) (c) 35,000
(D) (d) 43,000
✅ Answer & Explanation
Sahi jawab: A) (a) 53,000Explanation: Method 1 (100-Base Method): Total votes polled = 100%. Losing candidate = 35%. Winning candidate = 100% - 35% = 65%. Defeat margin = 65% - 35% = 30%. Given: 30% = 15900. 1% = \frac{15900}{30} = 530. Total votes polled (100%) = 530 \times 100 = 53000. Atah sahi vikalp (a) 53,000 hai. Method 2 (Ratio Method): Winner : Loser = 65 : 35 = 13 : 7. Margin = 13 - 7 = 6 units. 6 units = 15900 ==> 1 unit = \frac{15900}{6} = 2650. Total votes = 13 + 7 = 20 units = 20 \times 2650 = 53000. Atah sahi uttar (a) hai.
Vinod and Sanjay were fighting against each other for the post of a village Pradhan. Sanjay got 47.5% votes and lost the election by 270 votes. How many votes did Vinod get (assuming that all the villagers participated in the voting)?
विनोद और संजय ग्राम प्रधान के पद के लिए एक-दूसरे के खिलाफ चुनाव लड़ रहे थे। संजय को 47.5% मत मिले और वह 270 मतों से चुनाव हार गया। विनोद को कितने मत मिले (यह मानते हुए कि सभी ग्रामीणों ने मतदान में भाग लिया)?
(A) (a) 2385
(B) (b) 2835
(C) (c) 2565
(D) (d) 2655
✅ Answer & Explanation
Sahi jawab: B) (b) 2835Explanation: Method 1 (100-Base Method): Total votes = 100%. Sanjay = 47.5%. Vinod = 100% - 47.5% = 52.5%. Margin between them = 52.5% - 47.5% = 5%. Given: 5% = 270. 1% = \frac{270}{5} = 54. Votes obtained by Vinod (52.5%) = 52.5 \times 54 = 2835. Atah sahi vikalp (b) 2835 hai. Method 2 (Ratio Method): Vinod : Sanjay = 52.5 : 47.5 = 105 : 95 = 21 : 19. Margin = 21 - 19 = 2 units. 2 units = 270 ==> 1 unit = 135. Vinod's votes = 21 units = 21 \times 135 = 2835. Atah sahi uttar (b) hai.
In an election, the candidate who gets 90% votes is elected by a margin of 800 votes. What is the total number of votes cast? Note: Only two candidates are participating in the election and assume all votes are valid.
एक चुनाव में, 90% मत प्राप्त करने वाला उम्मीदवार 800 मतों के अंतर से चुना जाता है। डाले गए मतों की कुल संख्या क्या है? नोट: चुनाव में केवल दो उम्मीदवार भाग ले रहे हैं और मान लें कि सभी मत वैध हैं।
(A) (a) 900
(B) (b) 1000
(C) (c) 1050
(D) (d) 950
✅ Answer & Explanation
Sahi jawab: B) (b) 1000Explanation: Method 1 (100-Base Method): Total votes cast = 100%. Winner = 90% ==> Loser = 100% - 90% = 10%. Margin = 90% - 10% = 80%. Given: 80% = 800. 1% = \frac{800}{80} = 10. Total votes cast (100%) = 10 \times 100 = 1000. Atah sahi vikalp (b) 1000 hai. Method 2 (Ratio Method): Winner : Loser = 90 : 10 = 9 : 1. Margin = 9 - 1 = 8 units. 8 units = 800 ==> 1 unit = 100. Total votes = 9 + 1 = 10 units = 10 \times 100 = 1000. Atah sahi uttar (b) hai.
In an election between R and S, R gets 110% of the votes of S and beats S by 770 votes. If there were no invalid votes, then the total number of votes polled is:
R और S के बीच एक चुनाव में, R को S के मतों का 110% प्राप्त होता है और वह S को 770 मतों से हराता है। यदि कोई अमान्य मत नहीं था, तो डाले गए मतों की कुल संख्या है:
(A) (a) 17610
(B) (b) 17160
(C) (c) 16170
(D) (d) 16710
✅ Answer & Explanation
Sahi jawab: C) (c) 16170Explanation: Method 1 (Ratio Method): Let votes of S = 100 units. Then votes of R = 110% of 100 = 110 units. Ratio of R : S = 110 : 100 = 11 : 10. Margin by which R beats S = 11 - 10 = 1 unit. Given: 1 unit = 770. Total votes polled = 11 + 10 = 21 units. Total votes = 21 \times 770 = 16170. Atah sahi vikalp (c) 16170 hai. Method 2 (Algebraic Method): Let S get x votes, then R gets 1.10x votes. Difference = 1.10x - x = 0.10x = 770 ==> x = 7700. Total votes = x + 1.10x = 2.10x = 2.10 \times 7700 = 16170. Atah sahi uttar (c) hai.
A total of 7,50,000 voters participated in an election. A candidate received 3,82,500 votes which was 60% of the total valid votes. What was the percentage of invalid votes in the election?
एक चुनाव में कुल 7,50,000 मतदाताओं ने भाग लिया। एक उम्मीदवार को 3,82,500 मत प्राप्त हुए जो कुल वैध मतों का 60% था। चुनाव में अमान्य मतों का प्रतिशत क्या था?
(A) (a) 15%
(B) (b) 20%
(C) (c) 12%
(D) (d) 18%
✅ Answer & Explanation
Sahi jawab: A) (a) 15%Explanation: Method 1 (Valid Votes to Invalid Percentage Method): Candidate received 60% of Valid Votes = 382500. Total Valid Votes = \frac{382500}{60} \times 100 = 637500. Invalid Votes = Total Votes - Valid Votes = 750000 - 637500 = 112500. Percentage of invalid votes = \frac{112500}{750000} \times 100% = 15%. Atah sahi vikalp (a) 15% hai. Method 2 (Ratio Method): Candidate's votes / Total votes = \frac{382500}{750000} = 51%. Since Candidate got 60% of Valid Votes: 60% of Valid Votes = 51% of Total Votes. Valid Votes = \frac{51%}{0.60} = 85% of Total Votes. Invalid Votes = 100% - 85% = 15%. Atah sahi uttar (a) hai.
In an election, 95% of the total voters cast their votes. In this election, there were only two candidates A and B. The winner A, by obtaining 75% of the total votes, defeated his contestant B by 5500 votes. Find the total number of voters in the election.
एक चुनाव में कुल मतदाताओं में से 95% ने अपने मत डाले। इस चुनाव में केवल दो उम्मीदवार A और B थे। विजेता A ने कुल मतों का 75% प्राप्त करके अपने प्रतिद्वंद्वी B को 5500 मतों से हराया। चुनाव में मतदाताओं की कुल संख्या ज्ञात कीजिए।
(A) (a) 11,000
(B) (b) 10,000
(C) (c) 13,000
(D) (d) 12,000
✅ Answer & Explanation
Sahi jawab: B) (b) 10,000Explanation: Method 1 (100-Base Method): Let total voters registered = 100%. Total votes cast = 95%. A gets 75% of total votes = 75%. Votes obtained by B = Total cast - Votes of A = 95% - 75% = 20%. Winning margin = 75% - 20% = 55%. Given: 55% = 5500. 1% = \frac{5500}{55} = 100. Total number of voters (100%) = 100 \times 100 = 10000. Atah sahi vikalp (b) 10,000 hai. Method 2 (Ratio Method): A : B : Did not cast = 75 : 20 : 5 = 15 : 4 : 1. Margin between A and B = 15 - 4 = 11 units. Given: 11 units = 5500 ==> 1 unit = 500. Total voters = 15 + 4 + 1 = 20 units = 20 \times 500 = 10000. Atah sahi uttar (b) hai.
In an election, A received 27% of the votes and B received 125,982 votes. 19% did not cast their votes. Find the number of votes received by A.
एक चुनाव में, A को 27% मत प्राप्त हुए और B को 1,25,982 मत प्राप्त हुए। 19% लोगों ने अपने मत नहीं डाले। A द्वारा प्राप्त मतों की संख्या ज्ञात कीजिए।
(A) (a) 44,327
(B) (b) 1,88,973
(C) (c) 57,827
(D) (d) 62,991
✅ Answer & Explanation
Sahi jawab: D) (d) 62,991Explanation: Method 1 (100-Base Method): Total voters = 100%. A's votes = 27%. Did not vote = 19%. Percentage of votes received by B = 100% - (27% + 19%) = 100% - 46% = 54%. Given: 54% = 125982. 1% = \frac{125982}{54} = 2333. Number of votes received by A (27%) = 27 \times 2333 = 62991. Atah sahi vikalp (d) 62,991 hai. Method 2 (Ratio Method): Ratio of votes of A to B = 27% : 54% = 1 : 2. Since B has 2 units and A has 1 unit: A's votes = \frac{\text{B's votes}}{2} = \frac{125982}{2} = 62991. Atah sahi uttar (d) hai.
In an election between two candidates, one got 60% of the total valid votes, 90% of the votes were valid. If the total number of votes was 12000, then what was the number of valid votes that the other candidate got?
दो उम्मीदवारों के बीच एक चुनाव में, एक को कुल वैध मतों का 60% प्राप्त हुआ, 90% मत वैध थे। यदि मतों की कुल संख्या 12000 थी, तो दूसरे उम्मीदवार को प्राप्त वैध मतों की संख्या क्या थी?
(A) (a) 8840
(B) (b) 4320
(C) (c) 10800
(D) (d) 6200
✅ Answer & Explanation
Sahi jawab: B) (b) 4320Explanation: Method 1 (Step-by-Step Multiplication): Total votes = 12000. Valid votes = 90% of 12000 = 10800. Other candidate's valid votes = (100% - 60%) of 10800 = 40% of 10800 = 4320. Atah sahi vikalp (b) 4320 hai. Method 2 (Ratio Method): Other candidate's share = 12000 \times \frac{90}{100} \times \frac{40}{100} = 12000 \times \frac{9}{10} \times \frac{2}{5} = 4320. Atah sahi uttar (b) hai.
In an election between two candidates, 15% of the votes were invalid and one candidate got 52% of the total valid votes. If the total number of votes was 8000, what was the number of valid votes that the other candidate got?
दो उम्मीदवारों के बीच एक चुनाव में, 15% मत अमान्य थे और एक उम्मीदवार को कुल वैध मतों का 52% प्राप्त हुआ। यदि मतों की कुल संख्या 8000 थी, तो दूसरे उम्मीदवार को प्राप्त वैध मतों की संख्या क्या थी?
(A) (a) 3840
(B) (b) 3536
(C) (c) 6800
(D) (d) 3264
✅ Answer & Explanation
Sahi jawab: D) (d) 3264Explanation: Method 1 (Step-by-Step Percentage Method): Total votes = 8000. Invalid votes = 15% of 8000 = 1200. Valid votes = 8000 - 1200 = 6800. First candidate got 52% of valid votes, so the other candidate got: 100% - 52% = 48% of valid votes. Other candidate's valid votes = 48% of 6800 = \frac{48}{100} \times 6800 = 3264. Atah sahi vikalp (d) 3264 hai. Method 2 (Direct Fraction Multiplier): Other candidate's votes = 8000 \times (1 - 0.15) \times (1 - 0.52) = 8000 \times 0.85 \times 0.48 = 3264. Atah sahi uttar (d) hai.
In an election between two candidates, 10% of the registered voters did not cast their vote. The winning candidate got 60% of the total votes cast and defeated the other candidate by 1242 votes. Find the total number of registered voters.
दो उम्मीदवारों के बीच एक चुनाव में, पंजीकृत मतदाताओं में से 10% ने अपना मत नहीं डाला। जीतने वाले उम्मीदवार को डाले गए कुल मतों का 60% प्राप्त हुआ और उसने दूसरे उम्मीदवार को 1242 मतों से हराया। पंजीकृत मतदाताओं की कुल संख्या ज्ञात कीजिए।
(A) (a) 8640
(B) (b) 9600
(C) (c) 6200
(D) (d) 6900
✅ Answer & Explanation
Sahi jawab: D) (d) 6900Explanation: Method 1 (100-Base Method): Let registered voters = 100%. Votes cast = 100% - 10% = 90%. Winner got = 60% of votes cast = 0.60 \times 90% = 54% of registered voters. Loser got = 40% of votes cast = 0.40 \times 90% = 36% of registered voters. Winning margin = 54% - 36% = 18% of registered voters. Given: 18% = 1242. 1% = \frac{1242}{18} = 69. Total registered voters (100%) = 69 \times 100 = 6900. Atah sahi vikalp (d) 6900 hai. Method 2 (Ratio Method): Margin = \frac{1}{5} \times \text{Votes Cast} = 1242 ==> Votes Cast = 1242 \times 5 = 6210. Registered voters = 6210 \times \frac{10}{9} = 6900. Atah sahi uttar (d) hai.
In an election between two candidates, one got 65% of the total valid votes. 20% of the votes were invalid. If the total number of votes was 7,500, the number of valid votes that the other candidate got was:
दो उम्मीदवारों के बीच एक चुनाव में, एक को कुल वैध मतों का 65% प्राप्त हुआ। 20% मत अमान्य थे। यदि मतों की कुल संख्या 7,500 थी, तो दूसरे उम्मीदवार को प्राप्त वैध मतों की संख्या थी:
(A) (a) 4,300
(B) (b) 1,700
(C) (c) 1,900
(D) (d) 2,100
✅ Answer & Explanation
Sahi jawab: D) (d) 2,100Explanation: Method 1 (Step-by-Step Method): Total votes = 7500. Valid votes = 80% of 7500 = 6000. Other candidate received = 100% - 65% = 35% of valid votes. Other candidate's valid votes = 35% of 6000 = \frac{35}{100} \times 6000 = 2100. Atah sahi vikalp (d) 2,100 hai. Method 2 (Ratio Method): Valid votes = \frac{4}{5} \times 7500 = 6000. Candidate 2's share = 6000 \times \frac{35}{100} = 2100. Atah sahi uttar (d) hai.
In an election between two candidates, Anant and Arvind, Anant got 55% of the total valid votes, and 20% of the votes were invalid. If the total number of votes was 30,000, find the number of valid votes that Arvind got.
दो उम्मीदवारों अनंत और अरविंद के बीच एक चुनाव में, अनंत को कुल वैध मतों का 55% प्राप्त हुआ, और 20% मत अमान्य थे। यदि मतों की कुल संख्या 30,000 थी, तो अरविंद को मिले वैध मतों की संख्या ज्ञात कीजिए।
(A) (a) 10800
(B) (b) 1080
(C) (c) 13200
(D) (d) 24000
✅ Answer & Explanation
Sahi jawab: A) (a) 10800Explanation: Method 1 (Step-by-Step Method): Total votes = 30000. Invalid votes = 20% of 30000 = 6000. Valid votes = 30000 - 6000 = 24000. Arvind got = 100% - 55% = 45% of valid votes. Arvind's valid votes = 45% of 24000 = \frac{45}{100} \times 24000 = 10800. Atah sahi vikalp (a) 10800 hai. Method 2 (Direct Fraction Multiplication): Arvind's votes = 30000 \times \frac{4}{5} \times \frac{45}{100} = 24000 \times 0.45 = 10800. Atah sahi uttar (a) hai.
In an election between two candidates, one got 60% of the total valid votes and 15% of the votes were invalid. If the total number of votes were 8400, the number of valid votes that the other candidate got were:
दो उम्मीदवारों के बीच एक चुनाव में, एक को कुल वैध मतों का 60% प्राप्त हुआ और 15% मत अमान्य थे। यदि मतों की कुल संख्या 8400 थी, तो दूसरे उम्मीदवार को प्राप्त वैध मतों की संख्या थी:
(A) (a) 2998
(B) (b) 2856
(C) (c) 3213
(D) (d) 3117
✅ Answer & Explanation
Sahi jawab: B) (b) 2856Explanation: Method 1 (Percentage Step Method): Total votes = 8400. Valid votes = 85% of 8400 = \frac{85}{100} \times 8400 = 7140. Other candidate's valid votes = 40% of 7140 = \frac{40}{100} \times 7140 = 2856. Atah sahi vikalp (b) 2856 hai. Method 2 (Ratio Method): Valid votes = 8400 \times \frac{17}{20} = 7140. Other candidate got \frac{2}{5} of valid votes = 7140 \times \frac{2}{5} = 2856. Atah sahi uttar (b) hai.
In an election between two candidates, one got 60% of the total valid votes. 25% of the votes were invalid. If the total number of votes was 15,000, then find the number of valid votes that the other candidate got.
दो उम्मीदवारों के बीच एक चुनाव में, एक को कुल वैध मतों का 60% प्राप्त हुआ। 25% मत अमान्य थे। यदि मतों की कुल संख्या 15,000 थी, तो दूसरे उम्मीदवार को प्राप्त वैध मतों की संख्या ज्ञात कीजिए।
(A) (a) 5,550
(B) (b) 4,500
(C) (c) 6,750
(D) (d) 5,000
✅ Answer & Explanation
Sahi jawab: B) (b) 4,500Explanation: Method 1 (Step-by-Step Method): Total votes = 15000. Valid votes = 75% of 15000 = \frac{3}{4} \times 15000 = 11250. Other candidate's valid votes = 40% of 11250 = \frac{2}{5} \times 11250 = 4500. Atah sahi vikalp (b) 4,500 hai. Method 2 (Direct Chain Fraction): Other candidate's votes = 15000 \times \frac{3}{4} \times \frac{2}{5} = 15000 \times \frac{3}{10} = 4500. Atah sahi uttar (b) hai.
In an election, there were only two candidates. 12% of the voters did not cast their votes. The winner by obtaining 60% of the total votes defeated his opposite contestant by 1200 votes. Find the total number of votes.
एक चुनाव में केवल दो उम्मीदवार थे। 12% मतदाताओं ने अपने मत नहीं डाले। विजेता ने कुल मतों का 60% प्राप्त करके अपने प्रतिद्वंद्वी को 1200 मतों से हराया। मतों की कुल संख्या ज्ञात कीजिए।
(A) (a) 3750
(B) (b) 3570
(C) (c) 4000
(D) (d) 5730
✅ Answer & Explanation
Sahi jawab: A) (a) 3750Explanation: Method 1 (100-Base Method): Let total registered voters = 100%. Total polled votes = 100% - 12% = 88%. Winner got 60% of the total votes = 60%. Loser's votes = 88% - 60% = 28%. Winning margin = 60% - 28% = 32% of total votes. Given: 32% = 1200. 1% = \frac{1200}{32} = 37.5. Total number of votes (100%) = 37.5 \times 100 = 3750. Atah sahi vikalp (a) 3750 hai. Method 2 (Equation Method): Margin = 0.60V - 0.28V = 0.32V = 1200. V = \frac{1200}{0.32} = 3750. Atah sahi uttar (a) hai.
In an election between two candidates, the first gets 75% of the total valid votes. If 20% votes are invalid among 2,48,000 votes, then how many votes were cast in the favour of the other candidate?
दो उम्मीदवारों के बीच एक चुनाव में, पहले उम्मीदवार को कुल वैध मतों का 75% प्राप्त होता है। यदि 2,48,000 मतों में से 20% मत अमान्य हैं, तो दूसरे उम्मीदवार के पक्ष में कितने मत पड़े?
(A) (a) 56600
(B) (b) 46800
(C) (c) 53800
(D) (d) 49600
✅ Answer & Explanation
Sahi jawab: D) (d) 49600Explanation: Method 1 (Step-by-Step Multiplication): Total votes = 2,48,000. Valid votes = 80% of 2,48,000 = 1,98,400. Other candidate gets = 100% - 75% = 25% of valid votes. Votes for other candidate = 25% of 1,98,400 = \frac{1}{4} \times 1,98,400 = 49,600. Atah sahi vikalp (d) 49600 hai. Method 2 (Direct Fraction Method): Other candidate's votes = 248000 \times \frac{4}{5} \times \frac{1}{4} = \frac{248000}{5} = 49600. Atah sahi uttar (d) hai.
In an election between two candidates, 75% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 9504 votes, which were 80% of the valid votes. Find the total number of votes enrolled in that election.
दो उम्मीदवारों के बीच एक चुनाव में, 75% मतदाताओं ने अपने मत डाले, जिनमें से 4% मत अमान्य घोषित कर दिए गए। एक उम्मीदवार को 9504 मत मिले, जो वैध मतों का 80% था। उस चुनाव में नामांकित कुल मतों की संख्या ज्ञात कीजिए।
(A) (a) 12,375
(B) (b) 12,672
(C) (c) 13,200
(D) (d) 16,500
✅ Answer & Explanation
Sahi jawab: D) (d) 16,500Explanation: Method 1 (Ratio / Step Backtrack Method): Total Valid votes = \frac{9504}{0.80} = 11,880. Votes cast = \frac{11880}{0.96} = 12,375. Total Enrolled = \frac{12375}{0.75} = 16,500. Atah sahi vikalp (d) 16,500 hai. Method 2 (Chain Multiplier Method): V \times \frac{3}{4} \times \frac{24}{25} \times \frac{4}{5} = 9504 V \times \frac{72}{125} = 9504 ==> V = \frac{9504 \times 125}{72} = 16500. Atah sahi uttar (d) hai.