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Consider the following two types of elections to determine which of two parties $A$ and $B$ forms the next government in the 2014 Indian elections. Assume for simplicity an Indian population of size $545545 (=545 * 1001)$. There are only two parties $A$ and $B$ and every citizen votes.

TYPE C: The country is divided into $545$ constituencies and each constituency has $1001$ voters. Elections are held for each constituency and a party is said to win a constituency if it receive a majority of the vote in that constituency. The party that wins the most constituencies forms the next government.

TYPE P: There are no constituencies in this model. Elections are held throughout the country and the party that wins the most votes (among $545545$ voters forms the government.

Which of the following is true?

  1. If the party forms the govt. by election TYPE C winning at least two-third of the constituencies, then it will also forms the govt. by election TYPE P.
  2. If a party forms govt. by election TYPE C, then it will also form the govt. by election TYPE P.
  3. If a party forms govt. by election TYPE P, then it will also form the govt. by election TYPE C.
  4. All of the above
  5. None of the above.
in Numerical Ability by Boss (30.8k points) | 203 views

1 Answer

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Minimum condition for Type C winning: if any party wins $273$ constituencies out of $545$ and with vote $501$ out of $1001$ for each.
Minimum condition for Type P winning: if any party wins $272773$ votes out of $545545$

Option A:

  • Type C : Let party $A$ wins $2/3$ of  constituencies i.e., $364$ wins by $1$ vote and $181$ loss by all vote $364\times 501 + 181\times 0 = 182364$
  • Type P : If $A$ wins it should have more than half of vote i.e., $272773$

$\qquad$ So, it is FALSE since $A$ got only $182364$ votes

Option B : Similar to option A

Option C:

  • Type P: Let $A$ win by $272773$ votes 
  • Type C: If $A$ wins $272$ constituencies with $1001$ votes and loss $272$ with $1001$ and $1$ constituency with $1000$ votes then, total received votes $=272\times 1001+272\times 0+1\times 1= 272773$. But $A$ lose the  election since $A$ won only $272$ constituencies out of $545$ 

So option E must be correct.  

by Boss (16.5k points)
edited by

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