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  • Directions for question : In 2022, on the occasion of their 450th year of being established, the Order of the Jesuit Missionaries, who founded

Directions for question :

In 2022, on the occasion of their 450th year of being established, the Order of the Jesuit Missionaries, who founded the chain of St Xavier’s Schools in India, decided to honour the Fathers as well as the Principles of their Indian schools who helped propagate quality education in India. 

For that, they had to choose one of the schools where they would carry out this landmark ceremony at. In the final contention were St Xavier’s Collegiate School Kolkata, St Xavier’s School Durgapur, St Xavier’s School Mumbai and St Xavier’s School Ranchi. St Xavier’s Schools in India as per rule had one Principal per school, and all the schools in India were represented by their individual Principals in the selection. 

The eventual winner was determined through several rounds of voting by all the Principles of all the St Xavier’s Schools. In any round of voting, the school receiving the minimum number of votes in that round got eliminated. The surviving St Xavier’s School after the last round of voting would get the chance to host the ceremony.

Each Principal was allowed to cast votes for at most two schools in all rounds of voting combined. Hence, a Principal would become ineligible to cast a vote in a given round if both the St Xavier’s Schools he voted for in earlier rounds were out of contention in that round of voting. A Principle was also ineligible to cast a vote in a round if the St Xavier’s School he represented was in contention in that round of voting. As long as the Principal was eligible, he had to vote for only one contesting St Xavier’s School in any round of voting.

The following incomplete table shows the information on St Xavier’s Schools that received the maximum and minimum votes in different rounds of voting, the number of votes cast in their favor, and the total votes that were cast in those rounds.

 

Round No

Total Votes

Maximum Votes

Minimum Votes

School

No of Votes

School

No of Votes

1

 

St Xavier's School Durgapur

42

St Xavier's Collegiate School Kolkata

21

2

127

St Xavier's School Ranchi

  

St Xavier's School Mumbai

38

3

114

        

 

The following facts were also known :

a) All the Principals who voted for St Xavier’s School Durgapur and St Xavier’s School Ranchi in round one went on doing so as long they were in contention

b) Three fourth of those Principals who voted for St Xavier’s School Mumbai in round one voted for St Xavier’s School Mumbai in round two

c) Those Principals who voted for St Xavier’s Collegiate School Kolkata in round one voted for either St Xavier’s School Ranchi or St Xavier’s School Mumbai in round two

d) Half of the Principals who voted for St Xavier’s School Mumbai in round one voted for St Xavier’s School Ranchi in round three

e) The difference in votes between the two contending schools in the last round was 2.

Question:

Assuming that all the Principals of all the St Xavier’s Schools in India had the right to vote to elect one of the schools where the Order of the Jesuit Missionaries in Rome would carry out the landmark ceremony on the 450th year of their establishment, how many St Xavier’s Schools were there in India in 2022 ?

 

Option: 1

127

 


Option: 2

128


Option: 3

130


Option: 4

148


Answers (1)

best_answer

We already have found that :

All the St Xavier’s Schools in India were represented by their individual Principals in the selection, with each school having one Principal each.

Let the number of St Xavier’s Schools in India be x.

Also, x number of St Xavier’s Schools had x number of Principles.

Total number of Principals who voted in round one was (x – 4), because the Principals of the four St Xavier’s Schools in contention could not vote. 

Total number of Principals who voted in round two was (x – 3), because in round two only three St Xavier’s Schools were in contention and hence three Principals could not vote. 

Hence, (x – 3) = 127 

or, x = 130

Hence, 130 St Xavier’s Schools were there in India in 2022 

 

Posted by

Devendra Khairwa

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