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

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
Disciple Donors Pilgrims Disciple 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:

What is the total number of people who entered the Belur Math on 22nd August 2022 at 6.30 am and 7.30 am ?

Option: 1

156


Option: 2

168


Option: 3

174


Option: 4

Cannot be determined 

 


Answers (1)

best_answer

96 Disciples stayed at the Belur Math for 3 to 4 hours

120 Donors stayed at the Belur Math for 2 to 3 hours

240 Pilgrims stayed at the Belur Math for 1 to 2 hours

Let us consider the Disciples first.

As per the incomplete record at the security counter on 22nd August 2022 of the entry and exit of the 96 Disciples at the different times when the entry and exit gates opened, we can conclude the following :

  Entry Exit
Disciples Donors Pilgrims Disciples Donors Pilgrims
6.30 am X   12 0    
7.30 am 60-x 48   0    
8.30 am 12 0   0 36 0
9.30 am 0     a 0 0
10.30 am 24 12   b   96
11.30 am 0   0 60-(a+b) 24  
12.30 pm 0   24 12 0 0
1.30 pm 0     24    
Total 96     96    

At 6.30 am and 7.30 am a total of 60 Disciples had entered, and at 9.30 am, 10.30 am and 11.30 am a total of 60 Disciples had exited the Math. 12 Disciples had also entered the Math at 8.30 am.

Let us consider the Donors secondly.

As per the incomplete record at the security counter on 22nd August 2022 of the entry and exit of the 120 Donors at the different times when the entry and exit gates opened, we can conclude the following :

  Entry Exit
Disciples Donors Pilgrims Disciples Donors Pilgrims
6.30 am   36 12   0  
7.30 am   48     0  
8.30 am   0     36 0
9.30 am 0 24     0 0
10.30am 24 12     48 96
11.30 am   0 0   24  
12.30 pm   0 24 12 0 0
1.30 pm   0   24 12  
Total   120     120  

At 6.30 am and 9.30 am, 36  and 24 Donors respectively had entered the Belur Math. At 10.30 am and 1.30 pm, 48 and 12 Donors had exited the Math.

Finally let us consider the Pilgrims.

As per the incomplete record at the security counter on 22nd August 2022 of the entry and exit of the 240 Pilgrims at the different times when the entry and exit gates opened, we can conclude the following :

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

At 8.30 am, 9.30 am and 10.30 am a total of 204 Pilgrims entered the Belur Math. At 7.30 am, 11.30 am and 1.30 pm, 12, 108 and 24 Pilgrims respectively exited the Math.

So 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 are 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 0
1.30 pm 0 0 0 24 12 24
Total 96 120 240 96 120 240

The total number of Disciples who entered the Belur Math on 22nd August 2022 at 6.30 am and 7.30 am = x+(60-x) = 60

The total number of Donors who entered the Belur Math on 22nd August 2022 at 6.30 am and 7.30 am = 36+48 = 84

The total number of Pilgrims who entered the Belur Math on 22nd August 2022 at 6.30 am and 7.30 am = 12+0 = 12

Hence, the total number of people who entered the Belur Math on 22nd August 2022 at 6.30 am and 7.30 am = 60+84+12 = 156

Posted by

chirag

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