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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:

What percentage of Principals who had voted for St Xavier’s Collegiate School Kolkata in round one voted for St Xavier’s School Mumbai in round two ?

 

Option: 1

75%

 


Option: 2

66.67%


Option: 3

62.5%


Option: 4

33.33%


Answers (1)

best_answer

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, total number of Principals who voted in round one = (x – 4) = 130 – 4 = 126.

Let y be the number of Principals who voted for St Xavier’s Collegiate School Kolkata in round one and for St Xavier’s School Mumbai in round two.

They could not vote anymore after round two, as by then both St Xavier’s Collegiate School Kolkata and St Xavier’s School Mumbai were eliminated by dint of minimum number of votes in the first two rounds.

Also in round three only two St Xavier’s Schools were in contention and hence two Principals could not vote

Hence, total number of Principals who voted in round three was (130 – 2 – y) = (128 – y) 

Hence, 128 – y = 114 or, y = 14

Point (c) says that 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.

Now 21 Principals voted for St Xavier’s Collegiate School Kolkata in round one. 

Out of them 14 voted for St Xavier’s School Mumbai in round two.

So the rest of (21 – 14) = 7 Principals must have voted for St Xavier’s School Ranchi in round two.

Hence the rest of the votes (38 – 14) = 24 in favour of St Xavier’s School Mumbai in round two must have been of those Principals who voted for St Xavier’s School Mumbai in round one.

But that was three fourth of those Principals who voted for St Xavier’s School Mumbai in round one, as per point (b).

Hence total number of votes for in favour of St Xavier’s School Mumbai in round one = 24*(4/3) = 32.

The rest one fourth, that is 32*(1/4) = 8 of the Principals who voted for St Xavier’s School Mumbai in round one must have voted for St Xavier’s School Ranchi in round two.

Hence in round one : 

Total votes cast = 126, 

St Xavier’s School Durgapur = 42 votes 

St Xavier’s Collegiate School Kolkata = 21 votes

St Xavier’s School Mumbai = 32 votes

Hence, St Xavier’s School Ranchi = 126 – (42+21+32) = 31 votes.

St Xavier’s Collegiate School Kolkata gets minimum votes and is eliminated.

In round two St Xavier’s School Durgapur will get the 42 votes of the same Principals who voted for it in round one, as per point (a).

In round two St Xavier’s School Mumbai will get the 24 votes which was three fourth of those Principals who voted for St Xavier’s School Mumbai in round one.

Added to that will be the 14 votes of the Principals who voted for St Xavier’s Collegiate School Kolkata in round one and for St Xavier’s School Mumbai in round two.

Hence, total votes for St Xavier’s School Mumbai in the second round will be (24 + 14) = 38, as is showing in the table given.

In round two St Xavier’s School Ranchi, as per point (a), will also get the 31 votes of the same Principals who voted for it in round one.

Added to that will be the votes of the 7 Principals who had voted for of St Xavier’s Collegiate School Kolkata in round one but voted for St Xavier’s School Ranchi in round two.

Also added will be the votes of the 8 Principals who voted for St Xavier’s School Mumbai in round one, but must have voted for St Xavier’s School Ranchi in round two.

Also added would be the 1 vote of the Principal of St Xavier’s Collegiate School Kolkata, who was ineligible to vote in round one as his school was in contention, but could do so in round two as his school had been eliminated in round one. His vote could not go to St Xavier’s School Mumbai as their votes had already tallied with the number given in the table.

Hence in round two : 

Total votes cast = 127 

St Xavier’s School Durgapur = 42 votes

St Xavier’s School Mumbai = 38 votes

St Xavier’s School Ranchi = (31+7+8+1) = 47 votes

St Xavier’s School Mumbai gets minimum votes and is eliminated.

As per point (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.

Hence the other half has to vote for St Xavier’s School Durgapur, as there are now only two schools in contention.

Value of half of the votes in favour of St Xavier’s School Mumbai in round one = (1/2)*32 = 16

Hence total votes in favour of St Xavier’s School Durgapur in round three = (42 + 16) = 58

Already 8 Principals who voted for St Xavier’s School Mumbai in round one have voted for St Xavier’s School Ranchi in round two, and they continue their support in round three.

Hence another (16 – 8) = 8 votes must have shifted in favour of St Xavier’s School Ranchi in round three such that point (d) could be fulfilled.

Also added would be the 1 vote of the Principal of St Xavier’s Mumbai, who was ineligible to vote in round one and two as his school was in contention, but could do so in round three, as his school had been eliminated in round two. His vote could not go to St Xavier’s School Durgapur, as otherwise the difference between the maximum and minimum votes could not have been 2, as per point (e).

Hence total votes in favour of St Xavier’s School Ranchi in round three = (47 + 8 + 1) = 56

Hence, in round three : 

Total votes cast = 114

St Xavier’s School Durgapur = 58 votes

St Xavier’s School Ranchi = 56 votes

St Xavier’s School Ranchi gets minimum votes and is eliminated.

The final venue for the landmark ceremony celebrating the occasion of the 450th year of establishment of the Order of the Jesuit Missionaries was St Xavier’s School Durgapur.

The completed table read as follows :

 

Round No

Total Votes

Maximum Votes

Minimum Votes

School

No of Votes

School

No of Votes

1

126 

St  Xavier's School Durgapur

42

St Xavier's Collegiate School Kolkata

21

2

127

St Xavier's School Ranchi

47

St Xavier's School Mumbai

38

3

114

St Xavier's School Durgapur

58

St Xavier's School Ranchi

56

The number of Principals who voted for St Xavier’s Collegiate School Kolkata in round one = 21

The number of Principals who voted for St Xavier’s Collegiate School Kolkata in round one and for St Xavier’s School Mumbai in round two = 14

Hence, the percentage of Principals who had voted for St Xavier’s Collegiate School Kolkata in round one and voted for St Xavier’s School Mumbai in round two = (14/21)*100 = 66.67%

 

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Sayak

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