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  • Directions for question : The headquarters of the Ramkrishna Mission and Ramkrishna Math founded by Swami Vivekananda, the disciple of Sri Ramk

Directions for question :

The headquarters of the Ramkrishna Mission and Ramkrishna Math founded by Swami Vivekananda, the disciple of Sri Ramkrishna Paramhansa, is located at the majestic Belur Math, on the banks of the Ganges, in Howrah. It is one of the largest philanthropic institutions of the world and a place of pilgrimage for truth seekers all over the world from different religious faiths, and has a lot of footfall on a daily basis.

In the morning session, Belur Math opens its gates to all from 6.30 am to 1.30 pm every day. Entry and exit gates open after every one hour interval from 6.30 am, that is at 7.30 am, 8.30 am, and so on till 1.30 pm. People can enter or exit the Math only at those times. At 1.30 pm all people in the Math will have to leave and the Math gets closed to re-open in the evening at 6.30 pm again.

Three types of people visit the Belur Math every day. They are a) Disciples of Sri Ramkrishna Paramhansa and Swami Vivekananda, b) Donors to the Ramkrishna Mission for their philanthropic activity, and c) Pilgrims from all class of society. It has been observed that the Disciples stay at the Math for either 3 or 4 hours, the Donors stay for either 2 or 3 hours, and the pilgrims stay for either 1 or 2 hours.

On the 22nd of August 2022, at 2.00 pm, it was observed from the records at the security counter beside the entry and exit gates that 96 Disciples, 120 Donors and 240 Pilgrims had visited the Math that day since the gates opened at 6.30 am. An incomplete record of the entry and exit of the three types of people at different times was also available as below :

  Entry Exit
Disciples Donors Pilgrims Disciples Donors Pilgrims
6.30 am     12      
7.30 am   48        
8.30 am   0     36 0
9.30 am 0       0 0
10.30 am 24 12       96
11.30 am     0   24  
12.30 pm     24 12 0 0
1.30 pm       24    

Question:

If the number of Pilgrims who entered Belur Math on 22nd August 2022 at 9.30 am was equal to the number of Pilgrims who entered the Math at 10.30 am, what could be the possible number of Pilgrims (from the options given) who entered the Math at 8.30 am ?

Option: 1

45


Option: 2

60


Option: 3

75


Option: 4

97


Answers (1)

best_answer

We already know that the complete data on 22nd August 2022 of the entry and exit of the 96 Disciples, 120 Donors and 240 Pilgrims at the different times when the entry and exit gates opened were as below :

  Entry Exit
  Disciples Donors Pilgrims Disciples Donors Pilgrims
             
6.30 am x 36 12 0 0 0
7.30 am 60-x 48 0 0 0 12
8.30 am 12 0 m 0 36 0
9.30 am 0 24 n a 0 0
10.30 am 24 12 204-(m+n) b 48 96
11.30 am 0 0 0 60-(a+b) 24 108
12.30 pm 0 0 24 12 0 2
1.30 pm 0 0 0 24 12 24
Total 96 120 240 96 120 240

The total number of Pilgrims who had entered the Belur Math on 22nd August 2022 at 8.30 am, 9.30 am and 10.30 am was 204

The number of Pilgrims who entered Belur Math at 9.30 am was equal to the number of Pilgrims who entered the Math at 10.30 am.

So the summation for the Pilgrims who entered the Math at 9.30 am and 10.30 am must be an even number.

204 is itself an even number. 

The subtraction of the summation from 204 will give us the number of Pilgrims who entered the Math at 8.30 am.

The result of the subtraction should also be even.

Out of all the options given, only 60 is an even number.

Hence, the possible number of Pilgrims (from the options given) who entered the Math on 22nd August 2022 at 8.30 am is 60

 

Posted by

sudhir.kumar

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