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The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?(1) 1,10,000(2) 1,50,000(3) 1,40,000(4) 1,20,000
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The number of votes not cast for the PNC Party increased by 25% in the...
Problem: The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?
Solution:
Let the number of votes cast for the PNC Party in the previous Assembly Polls be x.
Number of votes not cast for the PNC Party in the previous Assembly Polls = 2,60,000 - x
The number of votes not cast for the PNC Party in the National General Election = (1 + 25/100) (2,60,000 - x) = 3,25,000 - 1.25x
The number of votes cast for the PNC Party in the National General Election = 2,60,000 - (3,25,000 - 1.25x) = 1.65x - 65,000
Let the majority by which the PNC Party won the Assembly Polls be y.
The PNC Party lost the National General Election by a majority twice as large as that by which it had won the Assembly Polls. Therefore, the majority by which the PNC Party lost the National General Election = 2y.
Therefore, the number of votes cast for the PNC Party in the National General Election = (2,60,000 - 2y) / 2
Equating the two expressions for the number of votes cast for the PNC Party in the National General Election, we get:
1.65x - 65,000 = (2,60,000 - 2y) / 2
Multiplying both sides by 2, we get:
3.3x - 1,30,000 = 2,60,000 - 2y
2y = 3.3x - 3,90,000
y = 1.65x - 1,95,000
Therefore, the PNC Party won the Assembly Polls by a majority of y = 1.65x - 1,95,000.
Substituting this value of y in the expression for the number of votes cast for the PNC Party in the National General Election, we get:
1.65x - 65,000 = (2,60,000 - 2(1.65x - 1,95,000)) / 2
Solving this equation, we get:
x = 1,40,000
Therefore, the number of votes cast for the PNC Party in the previous Assembly Polls is 1,40,000.
Answer: (3) 1,40,000
Solution:
Let the number of votes cast for the PNC Party in the previous Assembly Polls be x.
Number of votes not cast for the PNC Party in the previous Assembly Polls = 2,60,000 - x
The number of votes not cast for the PNC Party in the National General Election = (1 + 25/100) (2,60,000 - x) = 3,25,000 - 1.25x
The number of votes cast for the PNC Party in the National General Election = 2,60,000 - (3,25,000 - 1.25x) = 1.65x - 65,000
Let the majority by which the PNC Party won the Assembly Polls be y.
The PNC Party lost the National General Election by a majority twice as large as that by which it had won the Assembly Polls. Therefore, the majority by which the PNC Party lost the National General Election = 2y.
Therefore, the number of votes cast for the PNC Party in the National General Election = (2,60,000 - 2y) / 2
Equating the two expressions for the number of votes cast for the PNC Party in the National General Election, we get:
1.65x - 65,000 = (2,60,000 - 2y) / 2
Multiplying both sides by 2, we get:
3.3x - 1,30,000 = 2,60,000 - 2y
2y = 3.3x - 3,90,000
y = 1.65x - 1,95,000
Therefore, the PNC Party won the Assembly Polls by a majority of y = 1.65x - 1,95,000.
Substituting this value of y in the expression for the number of votes cast for the PNC Party in the National General Election, we get:
1.65x - 65,000 = (2,60,000 - 2(1.65x - 1,95,000)) / 2
Solving this equation, we get:
x = 1,40,000
Therefore, the number of votes cast for the PNC Party in the previous Assembly Polls is 1,40,000.
Answer: (3) 1,40,000
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The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?(1) 1,10,000(2) 1,50,000(3) 1,40,000(4) 1,20,000 Related: Percentages questions with Answers?
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The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?(1) 1,10,000(2) 1,50,000(3) 1,40,000(4) 1,20,000 Related: Percentages questions with Answers? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?(1) 1,10,000(2) 1,50,000(3) 1,40,000(4) 1,20,000 Related: Percentages questions with Answers? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?(1) 1,10,000(2) 1,50,000(3) 1,40,000(4) 1,20,000 Related: Percentages questions with Answers?.
The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?(1) 1,10,000(2) 1,50,000(3) 1,40,000(4) 1,20,000 Related: Percentages questions with Answers? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?(1) 1,10,000(2) 1,50,000(3) 1,40,000(4) 1,20,000 Related: Percentages questions with Answers? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?(1) 1,10,000(2) 1,50,000(3) 1,40,000(4) 1,20,000 Related: Percentages questions with Answers?.
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