CAT Quantitative Aptitude Questions | CAT Percentages Problems - Integers

The question is from CAT Percentages. CAT exam is known to test on basics rather than high funda ideas and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. This is an interesting question on the topic percentages using integers. In this question, an election is conducted where a certain no. of people were about to vote but on election date some people were kidnapped and election results were biased due to it. We need to find the no. of people who finally voted.

Question 27 : In a local election, 2400 people were to vote for Party A or Party B. Party A was bound to win the election. However, on Election Day, one-third of the voters of Party A were kidnapped. Party B was also able to influence the remaining Party A voters and thus double the strength of its voters. In this way, Party A lost by a majority which was half of that by which it would have won had the elections been fair. How many people finally voted for Party A and Party B?

1. 600(A), 1200(B)
2. 300(A), 600(B)
3. 450(A), 900(B)
4. 600(A), 900(B)

Explanatory Answer

Method of solving this CAT Question from Percentages: Easiest way to solve this question is through options.

Option a) If 600 voted for A and 1200 voted for B then
Before influencing, A = 600 + 600 = 1200, B = 1200 – 600 = 600(As half of B’s vote were through influencing)
Before kidnapping, A = 1200 + a∗12 of 1200 = 1800 (As 1/3 of A’s voters were kidnapped which is half of the 2/3 that remained)
Thus, total voter initially = 1800 (A) + 600 (B) = 2400
Thus option a) fits the scenario given in the question completely.

The question is " How many people finally voted for Party A and Party B? "
600 would have voted for Party A, 1200 would have voted for Party B.

Hence, the answer is 600(A), 1200(B)

Choice A is the correct answer.