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Class I-V Tuition > Learn Mental Mathematics > In a village 70% cast their votes in an election. Only...
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In a village 70% cast their votes in an election. Only two candidates A and B contested the election. A won the election by 400 votes. Had A received 12.5% less votes, the resulted would have been tie. How many registered voters in village?

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Answer: 8571 Let the number of votes received by A and B be a and b, respectively. Then, b = a - 400 Also, a*87.5/100 = b a - 400 = 875a/1000 ⇒ 1000a - 400000 = 875a ⇒ 125a = 400000 ⇒ a = 3200 And, b = 3200 - 400 = 2800 Thus, Total votes casted = 3200 + 2800 = 6000 Number of registered...
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Answer: 8571 Let the number of votes received by A and B be a and b, respectively.Then, b = a - 400Also, a*87.5/100 = b a - 400 = 875a/1000⇒ 1000a - 400000 = 875a⇒125a = 400000⇒a = 3200And, b = 3200 - 400 = 2800 Thus, Total votes casted = 3200 + 2800 = 6000Number of registered voters = 6000*100/70 = 8571.43 But since it's the number of registered voters, which must be a whole number, so there are 8571 registered voters. read less
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Let us assume that B got 'x' number of votes. B got x number of votes.But, when A got (x + 400)/8 less votes then votes that B got = x + (x + 400)/8 = (8x + x + 400)/8 New number of votes that B got = (9x + 400)/8 ........(2) Now,there is tie when A would have got 12.5 %...
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Let us assume that B got 'x' number of votes. B got x number of votes.But, when A got (x + 400)/8 less votes then votes that B got = x + (x + 400)/8 = (8x + x + 400)/8 New number of votes that B got = (9x + 400)/8 ........(2) Now,there is tie when A would have got 12.5 % less votes.So, (1) = (2) (7x + 2800)/8 = (9x + 400)/8 56x + 22400 = 72x + 320056x - 72x = 3200 - 22400- 16x = - 19200x = 19200/16x = 1200 Number of that B got = 1200 And number of votes that A got = 1200 + 400 = 1600Total votes casted = 1200 + 1600 = 2800This is only 70 % of the total registered votes.Number of registered voters in the village = (2800*100)/70= 4000 read less
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Suppose candidate A gets x votes and candidate B gets y votes. Then - Equation 1 : x - y = 400 ...... (1) Had A received 12.5% less votes, the resulted would have been tie. Therefore- x - 25 / 2 × 1 / 100 x = y Which on simplification is 200 x - 25 x = 200 y OR ...
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Suppose candidate A gets x votes and candidate B gets y votes. Then - Equation 1 : x - y = 400 ...... (1) Had A received 12.5% less votes, the resulted would have been tie. Therefore- x - 25 / 2 × 1 / 100 x = y Which on simplification is 200 x - 25 x = 200 y OR 175 x = 200 y Or 175 x - 200 y = 0 ....... (2) Simplifying 1 & 2 , we get Candidate A(????) got 3200 votes & Candidate B (??) got 2800 votes. ANS : Total registered voters = 3200+2800=6000 {70 per cent cast their votes- is not required for solving the sum. It's to distract. Best to avoid the information in this sum} from Subhash Sir?? read less
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Registered votes=1600. 1120 cost their votes A get 760 votes, B get 360 votes
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Let us assume that B got 'x' number of votes.Then A got x + 400 number of votes.When if A gets 12.5 % fewer votes then the result would have been a tie.So, according to the question = {(x + 400)*12.5}/100= (x + 400)/8New number of votes that A got = (x + 400) - (x + 400)/8= (8x + 3200 - x - 400)8New...
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Let us assume that B got 'x' number of votes.Then A got x + 400 number of votes.When if A gets 12.5 % fewer votes then the result would have been a tie.So, according to the question = {(x + 400)*12.5}/100= (x + 400)/8New number of votes that A got = (x + 400) - (x + 400)/8= (8x + 3200 - x - 400)8New number of votes that A got = (7x + 2800)/8 ...........(1) Now, originally B got x number of votes.But, when A got (x + 400)/8 less votes then votes that B got = x + (x + 400)/8= (8x + x + 400)/8New number of votes that B got = (9x + 400)/8 ........(2)Now,there is tie when A would have got 12.5 % less votes.So, (1) = (2)(7x + 2800)/8 = (9x + 400)/856x + 22400 = 72x + 320056x - 72x = 3200 - 22400- 16x = - 19200x = 19200/16x = 1200Number of that B got = 1200And number of votes that A got = 1200 + 400 = 1600Total votes casted = 1200 + 1600 = 2800This is only 70 % of the total registered votes.Now,Number of registered voters in the village = (2800*100)/70= 4000Total registered voters in the village are 4000 read less
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Let no. of votes actually obtained by A and B be a and b. a is 400 more than b => a = b + 400 ........ (1) If a had got 12.5% less votes, b would have got more votes of the same number (as they are the pnly 2 candidates contesting). As this would have resulted in a tie, it implies that these...
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Let no. of votes actually obtained by A and B be a and b. a is 400 more than b => a = b + 400 ........ (1) If a had got 12.5% less votes, b would have got more votes of the same number (as they are the pnly 2 candidates contesting). As this would have resulted in a tie, it implies that these would have bridged the gap of 400 votes between them, i.e. 25% of a is 400 ....... (2) => a = 1600. b = a - 400 = 1200 So total number of votes polled is 2800. But this was just 70% of the total number of registered voters. So number of registered voters = 2800/0.7 = 4000. read less
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