Question 2: 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?
(a) 1,10,000
(b) 1,50,000
(c) 1,40,000
(d) 1,20,000
Answers
Answer and Explanation
Option c
Total Votes = 2,60,000
Let x voters voted against the party in the Assembly Poll.
Then votes in favour = 260000 – x
Therefore, majority of votes by which party won in previous poll = 260000– x – x = 260000 – 2x
Next year votes against the PNC party increase by 25%
So, votes against the party in general election = 1.25 x
And votes polled in favour of the party = total votes – votes against = 260000 – 1.25x
Therefore, majority of votes by which party lost in general election
= 1.25x – (260000 – 1.25x) = 2.5x – 260000
It is given that, PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls, Therefore
2.5x – 260000 = 2(260000 – 2 x)
⇒ 2.5x – 260000 = 2 260000 – 4x
⇒ 6.5x = 3260000⇒x == 1,20,000
Therefore, votes polled by the voters for the party in Assembly Polls for previous year
= (2,60,000 – x) = (2,60,000 – 1,20,000) = 1,40,000.
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