The number of votes not cast for the Praja Party increased by 25\% in the National General Election over those not cast for it in the previous Assembly polls and the Praja Party lost by a majority twice as large as that by which it had won the previous Assembly polls. If a total 2,60,000 people voted each time how many voted for the Praja Party in the previous Assembly polls?
(a)110000
(b)120000
(c)140000
(d)150000
Answer
Answer (as printed): C
Explanation
Let $x$ be the number of votes not cast for the Praja Party in the previous polls. So, number of votes not cast for the party this year $=1.25 x$. Then, number of votes cast for Praja party in the previous polls $=(260000-x)$. Number of votes cast for the party this year $=(260000-$ 1.25x). Margin of victory in previous polls = (Votes cast in favour) - (Votes not cast in favour) $$=(260000-x)-x=(260000-2 x) .$$ Margin of loss in this year's polls = (Votes not cast in favour) - (Votes cast in favour) $$=1.25 x-(260000-1.25 x)=2.5 x-260000 . \begin{aligned} \therefore \quad 2.5 x & -260000 \\ & =2(260000-2 x) \Rightarrow 6.5 x=780000 \Rightarrow x=120000 . \end{aligned}$$ Hence, number of people who voted for Praja Party in previous polls $=260000-120000=140000$.
Explanation as extracted from the printed page; notation may be imperfect.