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In the audition held in 1969 for the actors of the Satyajit Ray Bengali language classic ‘Aranyer Din-Ratri’, twenty five of the top actors of Bengali cinema took part. A merit list was prepared based on their score in the audition. The actor with the highest score got the first rank and the one with the lowest score the last rank. None of the twenty five actors had the same score in the audition.

Five actors – Mr Soumitra Chattopadhyay, Dr Subhendu Chattopadhyay, Mr Shamit Bhanja, Mr Pahari Sanyal and Mr Rabi Ghosh – who had appeared for the audition gave the following clues about their ranks when asked for it :

a) For all five of them, the number of actors having a higher score than an actor was not the same as the number of actors having a lower score than that actor, or for that matter, any other actor 

b) Mr Shamit Bhanja had a higher score than Dr Subhendu Chattopadhyay, who in turn had a higher score than Mr Pahari Sanyal

c) The number of actors between Mr Pahari Sanyal and Mr Shamit Bhanja in the merit list was the same as the number of actors between Mr Soumitra Chattopadhyay and Dr Subhendu Chattopadhyay.

d) At least sixteen actors got a higher score than Mr Soumitra Chattopadhyay

e) The number of actors having a lower score than Mr Pahari Sanyal was at least fifteen, which was at most seven more than the number of actors than those who had a higher score than him

f) The number of actors ranked between Mr Pahari Sanyal and Mr Rabi Ghosh was twice the number of students ranked between Mr Pahari Sanyal and Mr Soumitra Chattopadhyay

Question

How many actors had a lower score than Dr Subhendu Chattopadhyay ?

 

Option: 1

17


Option: 2

11


Option: 3

13


Option: 4

15


Answers (1)

best_answer

From (d) we can conclude that the rank of Mr Soumitra Chattopadhyay ranged from 17th to 25th.

Let the number of actors having a score lower than Mr Pahari Sanyal be x.

It is given in (e) that x was >/= 15

Let the number of actors having a score higher than Mr Pahari Sanyal be y.

But then x had to be at most seven more than y (e).

Thus y could be either (x-7) or (x-6) or (x-5) or (x-4) or (x-3) or (x-2) or (x-1)

The total number of actors who had auditioned for ‘Aranyer Din-Ratri’ = 25

Case 1 : x + 1 + (x-7) = 25 or, x = 15.5. This case was not possible as x cannot be a fraction

Case 2 : x + 1 + (x-6) = 25 or, x = 15. This case was possible. Thus x = 15 means y = (15-6) = 9

Case 3 : x + 1 + (x-5) = 25 or, x = 14.5. This case was not possible as x cannot be a fraction

Case 4 : x + 1 + (x-4) = 25 or, x = 14. This case was not possible as x was >/= 15

Case 5 : x + 1 + (x-3) = 25 or, x = 13.5. This case was not possible as x cannot be a fraction

Case 6 : x + 1 + (x-2) = 25 or, x = 13. This case was not possible as x was >/= 15

Case 7 : x + 1 + (x-1) = 25 or, x = 12.5. This case was not possible as x cannot be a fraction

Thus Mr Pahari Sanyal’s rank was 10th.

From (b), Mr Shamit Bhanja had a higher score than Dr Subhendu Chattopadhyay, who in turn had a higher score than Mr Pahari Sanyal. 

So the range of the ranks of Mr Shamit Bhanja was from 1st to 8th, while that of Dr Subhendu Chattopadhyay was from 2nd to 9th.

The number of actors ranked between Mr Pahari Sanyal and Mr Shamit Bhanja in the merit list could be a minimum of 1 (as Dr Subhendu Chattopadhyay was between them), and a maximum of 8 (if Mr Shamit Bhanja had the 1st rank).

The number of actors ranked between Dr Subhendu Chattopadhyay and Mr Soumitra Chattopadhyay could be a minimum of (17-10) = 7 (if Dr Subhendu Chattopadhyay had the 9th rank and Mr Soumitra Chattopadhyay had the 17th rank) and a maximum of (25-3) = 22 (if Dr Subhendu Chattopadhyay had the 2nd rank and Mr Soumitra Chattopadhyay had the 25th rank)

But in (c) it is given that the number of actors between Mr Pahari Sanyal and Mr Shamit Bhanja in the merit list was the same as the number of actors between Mr Soumitra Chattopadhyay and Dr Subhendu Chattopadhyay.

So from the two deductions in the previous paragraph, we can be sure that the number of actors between them could be either 7 or 8 only.

Case 1 : Number of actors between them = 7

This case ensures that Dr Subhendu Chattopadhyay had the 9th rank and Mr Soumitra Chattopadhyay had the 17th rank, and simultaneously Mr Shamit Bhanja had the 2nd rank and Mr Pahari Sanyal had the 10th rank as we already know

The second situation was possible.

But the first situation implied that (9-1) = 8 actors had a higher score than Dr Subhendu Chattopadhyay, and (25-17) = 8 actors had a lower score than Mr Soumitra Chattopadhyay.

This violated condition (a) which states that for all five of the actors, the number of actors having a higher score than an actor was not the same as the number of actors having a lower score than that actor, or for that matter, any other actor 

So Case 1 as a whole is rendered impossible.

Case 2 : Number of actors between them = 8

This case ensures that 

A) Mr Shamit Bhanja had the 1st rank with Mr Pahari Sanyal as the 10th rank, and simultaneously Dr Subhendu Chattopadhyay had the 9th rank and Mr Soumitra Chattopadhyay had the 18th rank, or,

B) Mr Shamit Bhanja had the 1st rank with Mr Pahari Sanyal as the 10th rank, and simultaneously Dr Subhendu Chattopadhyay had the 8th rank and Mr Soumitra Chattopadhyay had the 17th rank

Case 2A: 

Number of actors between Mr Pahari Sanyal (10th rank) and Mr Soumitra Chattopadhyay (18th rank) = 7

Hence, as per condition (f), the number of actors ranked between Mr Pahari Sanyal and Mr Rabi Ghosh = 2*7 = 14

Thus the rank of Mr Rabi Ghosh = 25th

But Mr Shamit Bhanja had the 1st rank

So zero actors had a score better than Mr Shamit Bhanja and zero actors had a score less than Mr Rabi Ghosh, which violated condition (a) which states that for all five of the actors, the number of actors having a higher score than an actor was not the same as the number of actors having a lower score than that actor, or for that matter, any other actor

So Case 2A is rendered impossible

Case 2B : 

Number of actors between Mr Pahari Sanyal (10th rank) and Mr Soumitra Chattopadhyay (17th rank) = 6

Hence, as per condition (f), the number of actors ranked between Mr Pahari Sanyal and Mr Rabi Ghosh = 2*6 = 12

Thus the rank of Mr Rabi Ghosh = 23rd

No conditions are violated.

So Case 2B is possible

Hence finally, the rankings of the five actors in the audition held in 1969 for the actors of the Satyajit Ray Bengali language classic ‘Aranyer Din-Ratri’ were as follows :

Mr Shamit Bhanja = 1st rank

Dr Subhendu Chattopadhyay = 8th rank

Mr Pahari Sanyal = 10th rank

Mr Soumitra Chattopadhyay = 17th rank

Mr Rabi Ghosh = 23rd rank

Hence the number of actors who had a lower score, and hence a lower ranking than Dr Subhendu Chattopadhyay = 17.

 

Posted by

Ritika Jonwal

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