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  • Directions for question: Behala Players’ Corner is a registered club known for its grand public annual Durga Puja celebration held at Beh

Directions for question:

Behala Players’ Corner is a registered club known for its grand public annual Durga Puja celebration held at Behala Chowrasta, Kolkata, under the patronage of the family of Mr Chandidas Ganguly, whose sons Mr Snehasis Ganguly and Mr Sourav Ganguly are notable members.

Mr Abhik Mishra, Mr Biplab Das, Mr Chinmoy Sen and Mr Dilip Palit, all of whom were very reputed and well-to-do local residents are actively involved every year as volunteers in collecting subscriptions on behalf of Behala Players’ Corner for the expenditure of Durga Puja celebrations. They are cumulatively entrusted with the responsibility of subscriptions from the four localities of Barisha, Bakultala, Sarsuna and Adarshapally, all areas being in the vicinity of Behala Players’ Corner.

The following partially filled table shows the subscriptions collected by each of them in the month of September 2021, a month before Durga Puja :

 

 

Total Cumulative Subscription from four localities

Maximum Cumulative Subscription from any locality

Cumulative Subscription from Barisha

Cumulative Subscription from Bakultala

Cumulative Subscription from Sarsuna

Cumulative Subscription from Adarshapally

Mr Abhik Mishra

Rs 4,11,600

Rs 1,17,600

Rs 74,400

 

 

 

Mr Biplab Das

Rs 2,78,400

Rs 91,200

 

 

 

Rs 21,600

Mr Chinmoy Sen

Rs 3,45,600

Rs 1,12,800

Rs 36,000

 

 

 

Mr Dilip Palit

Rs 1,29,600

Rs 57,600

 

 

 

Rs 14,400

TOTAL

Rs 11,65,200

 

Rs 2,44,800

Rs 3,44,400

Rs 3,28,800

Rs 2,47,200

 

It was also known that :

a) Each volunteer collected the maximum cumulative subscription from distinct localities out of the four. 

b) No volunteer collected equal subscriptions from any two localities.

c) Mr Biplab Das collected more subscriptions from Bakultala than Sarsuna.

d) The subscription collected by all four volunteers from each locality was a multiple of Rs 1,200.

Question:

What was the difference (in Rs) between the amounts collected as subscription by Mr Biplab Das from Barisha and Adarshapally ?

 

Option: 1

55,200

 


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

From the first condition given, we know that each volunteer collected the maximum cumulative subscription from distinct localities out of the four.

Hence, considering the four different arrangements that the above condition produces, there are four Cases, named Case 1A, 1B, 2A and 2B respectively as shown below.

The selection of the maximum cumulative subscription from distinct localities is shaded in green, the resultant second phase of calculation by column wise addition and subtraction is shaded in yellow, and the resultant third phase of calculation by further row wise addition and subtraction is shaded in pink.

 

CASE 1A

Total Cumulative Subscription from four localities

Maximum Cumulative Subscription from any locality

Cumulative Subscription from Barisha

Cumulative Subscription from Bakultala

Cumulative Subscription from Sarsuna

Cumulative Subscription from Adarshapally

Mr Abhik Mishra

Rs 4,11,600

Rs 1,17,600

Rs 74,400

Rs 1,17,600

Rs 1,21,200

Rs 98,400

Mr Biplab Das

Rs 2,78,400

Rs 91,200

Rs 91,200

 

 

Rs 21,600

Mr Chinmoy Sen

Rs 3,45,600

Rs 1,12,800

Rs 36,000

 

 

Rs 1,12,800

Mr Dilip Palit

Rs 1,29,600

Rs 57,600

Rs 43,200

Rs 14,400

Rs 57,600

Rs 14,400

TOTAL

Rs 11,65,200

 

Rs 2,44,800

Rs 3,44,400

Rs 3,28,800

Rs 2,47,200



 

CASE 1B

Total Cumulative Subscription from four localities

Maximum Cumulative Subscription from any locality

Cumulative Subscription from Barisha

Cumulative Subscription from Bakultala

Cumulative Subscription from Sarsuna

Cumulative Subscription from Adarshapally

Mr Abhik Mishra

Rs 4,11,600

Rs 1,17,600

Rs 74,400

Rs 1,21,200

Rs 1,17,600

Rs 98,400

Mr Biplab Das

Rs 2,78,400

Rs  91,200

Rs 91,200

 

 

Rs 21,600

Mr Chinmoy Sen

Rs 3,45,600

Rs 1,12,800

Rs 36,000

 

 

Rs 1,12,800

Mr Dilip Palit

Rs 1,29,600

Rs 57,600

Rs 43,200

Rs 57,600

Rs 14,400

Rs 14,400

TOTAL

Rs 11,65,200

 

Rs 2,44,800

Rs 3,44,400

Rs 3,28,800

Rs 2,47,200



 

CASE 2A

Total Cumulative Subscription from four localities

Maximum Cumulative Subscription from any locality

Cumulative Subscription from Barisha

Cumulative Subscription from Bakultala

Cumulative Subscription from Sarsuna

Cumulative Subscription from Adarshapally

Mr Abhik Mishra

Rs 4,11,600

Rs 1,17,600

Rs 74,400

 

 

Rs 1,17,600

Mr Biplab Das

Rs 2,78,400

Rs 91,200

Rs 76,800

Rs 91,200

Rs 88,800

Rs 21,600

Mr Chinmoy Sen

Rs 3,45,600

Rs 1,12,800

Rs 36,000

Rs 1,03,200

Rs 1,12,800

Rs 93,600

Mr Dilip Palit

Rs 1,29,600

Rs 57,600

Rs 57,600

 

 

Rs 14,400

TOTAL

Rs 11,65,200

 

Rs 2,44,800

Rs 3,44,400

Rs 3,28,800

Rs 2,47,200



 

CASE 2B

Total Cumulative Subscription from four localities

Maximum Cumulative Subscription from any locality

Cumulative Subscription from Barisha

Cumulative Subscription from Bakultala

Cumulative Subscription from Sarsuna

Cumulative Subscription from Adarshapally

Mr Abhik Mishra

Rs 4,11,600

Rs 1,17,600

Rs 74,400

 

 

Rs 1,17,600

Mr Biplab Das

Rs 2,78,400

Rs 91,200

Rs 76,800

Rs 88,800

Rs 91,200

Rs 21,600

Mr Chinmoy Sen

Rs 3,45,600

Rs 1,12,800

Rs 36,000

Rs 1,12,800

Rs 1,03,200

Rs 93,600

Mr Dilip Palit

Rs 1,29,600

Rs 57,600

Rs 57,600

 

 

Rs 14,400

TOTAL

Rs 11,65,200

 

Rs 2,44,800

Rs 3,44,400

Rs 3,28,800

Rs 2,47,200


 

But Case 1A is not possible. 

Because Mr Abhik Mishra had a maximum cumulative collection of Rs 1,17,600, while his collection at Sarsuna comes out to Rs 1,21,200, which is impossible. Also in the second condition it is given that no volunteer collected equal subscriptions from any two localities. But that is exactly what results with Mr Dilip Palit at Bakultala and Adarshapally.

Case 1B is also not possible.

Because Mr Abhik Mishra had a maximum cumulative collection of Rs 1,17,600, while his collection at Bakultala comes out to Rs 1,21,200, which is impossible. Also in the second condition it is given that no volunteer collected equal subscriptions from any two localities. But that is exactly what results with Mr Dilip Palit at Sarsuna and Adarshapally.

Case 2B is also not possible.

In the third condition it is given that Mr Biplab Das collected more subscription from Bakultala than Sarsuna. But here his collection at Bakultala (Rs 88,800) is less than the collection at Sarsuna (Rs 91,200).

So, only Case 2A is possible.

Let the unknown subscriptions of Mr Abhik Mishra and Mr Dilip Palit in Case 2A be denoted by m, n, o and p as shown below :

 

CASE 2A

Total Cumulative Subscription from four localities

Maximum Cumulative Subscription from any locality

Cumulative Subscription from Barisha

Cumulative Subscription from Bakultala

Cumulative Subscription from Sarsuna

Cumulative Subscription from Adarshapally

Mr Abhik Mishra

Rs 4,11,600

Rs 1,17,600

Rs 74,400

m

n

Rs 1,17,600

Mr Biplab Das

Rs 2,78,400

Rs 91,200

Rs 76,800

Rs 91,200

Rs 88,800

Rs 21,600

Mr Chinmoy Sen

Rs 3,45,600

Rs 1,12,800

Rs 36,000

Rs 1,03,200

Rs 1,12,800

Rs 93,600

Mr Dilip Palit

Rs 1,29,600

Rs 57,600

Rs 57,600

o

p

Rs 14,400

TOTAL

Rs 11,65,200

 

Rs 2,44,800

Rs 3,44,400

Rs 3,28,800

Rs 2,47,200

 

Hence, 

m + n = 411600 – (74400+117600) = Rs 2,19,600

o + p = 129600 – (57600+14400) = Rs 57,600

m + o = 344400 – (91200+103200) = Rs 1,50,000

n + p = 328800 – (88800+112800) = Rs 1,27,200

In the third condition it is given that the subscription collected by all four volunteers from each locality was a multiple of Rs 1,200.

Hence the upper limit of m or n is 117600 – 1200 = Rs 1,16,400, and will decrease with a difference of Rs 1,200.

The lower limit of n or m is 74400 + 1200 = Rs 75,600, and will increase with a difference of Rs 1,200.

Also the upper limit of o + p = 57600 – 1200 = Rs 56,400, and will decrease with a difference of Rs 1,200.

The lower limit of p + o = 14400 + 1200 = Rs 15,600, and will increase with a difference of Rs 1,200.

 

Hence the probable twelve values of m, n, o and p can be as follows :

 

 

m

n

o

p

1

Rs 1,16,400

(219600-116400)                   = Rs 1,03,200

(150000-116400)                   = Rs 33,600

(57600-33600)                         = Rs 24,000

2

Rs 1,03,200

Rs 1,16,400

(150000-103200)                   = Rs 46,800

(57600-46800)                         = Rs 10,800

3

Rs 1,15,200

(219600-115200)                   = Rs 1,04,400

(150000-115200)                   = Rs 34,800

(57600-34800)                         = Rs 22,800

4

Rs 1,04,400

Rs 1,15,200

(150000-104400)                   = Rs 45,600

(57600-45600)                         = Rs 12,000

5

Rs 1,14,000

(219600-114000)                   = Rs 1,05,600

(150000-114000)                   = Rs 36,000

(57600-36000)                         = Rs 21,600

6

Rs 1,05,600

Rs 1,14,000

(150000-105600)                   = Rs 44,400

(57600-44400)                         = Rs 13,200

7

Rs 1,12,800

(219600-112800)                   = Rs 1,06,800

(150000-112800)                   = Rs 37,200

(57600-37200)                         = Rs 20,400

8

Rs 1,06,800

Rs 1,12,800

(150000-106800)                   = Rs 43,200

(57600-43200)                         = Rs 14,400

9

Rs 1,11,600

(219600-111600)                   = Rs 1,08,000

(150000-111600)                   = Rs 38,400

(57600-38400)                         = Rs 19,200

10

Rs 1,08,000

Rs 1,11,600

(150000-108000)                   = Rs 42,000

(57600-42000)                         = Rs 15,600

11

Rs 1,10,400

(219600-110400)                   = Rs 1,09,200

(150000-110400)                   = Rs 39,600

(57600-39600)                         = Rs 18,000

12

Rs 1,09,200

Rs 1,10,400

(150000-109200)                   = Rs 40,800

(57600-40800)                         = Rs 16,800

 

However numbers 2, 4, 6 and 8 cannot be probable values as the value of p becomes less than or equal to the lowest subscription collected by Mr Dilip Palit from any locality.

Hence the final figures of all the subscriptions collected by the four volunteers from the four localities are :

 

CASE 2A

Total Cumulative Subscription from four localities

Maximum Cumulative Subscription from any locality

Cumulative Subscription from Barisha

Cumulative Subscription from Bakultala

Cumulative Subscription from Sarsuna

Cumulative Subscription from Adarshapally

Mr Abhik Mishra

Rs 4,11,600

Rs 1,17,600

Rs 74,400

m

n

Rs 1,17,600

Mr Biplab Das

Rs 2,78,400

Rs 91,200

Rs 76,800

Rs 91,200

Rs 88,800

Rs 21,600

Mr Chinmoy Sen

Rs 3,45,600

Rs 1,12,800

Rs 36,000

Rs 1,03,200

Rs 1,12,800

Rs 93,600

Mr Dilip Palit

Rs 1,29,600

Rs 57,600

Rs 57,600

o

p

Rs 14,400

TOTAL

Rs 11,65,200

 

Rs 2,44,800

Rs 3,44,400

Rs 3,28,800

Rs 2,47,200

 

with the eight different combination of values of m, n, o and p being :

 

 

m

n

o

p

1

Rs 1,16,400

Rs 1,03,200

Rs 33,600

Rs 24,000

2

Rs 1,15,200

Rs 1,04,400

Rs 34,800

Rs 22,800

3

Rs 1,14,000

Rs 1,05,600

Rs 36,000

Rs 21,600

4

Rs 1,12,800

Rs 1,06,800

Rs 37,200

Rs 20,400

5

Rs 1,11,600

Rs 1,08,000

Rs 38,400

Rs 19,200

6

Rs 1,08,000

Rs 1,11,600

Rs 42,000

Rs 15,600

7

Rs 1,10,400

Rs 1,09,200

Rs 39,600

Rs 18,000

8

Rs 1,09,200

Rs 1,10,400

Rs 40,800

Rs 16,800

 

Hence, the difference (in Rs) between the amounts collected as subscription by Mr Biplab Das from Barisha and Adarshapally

= 76800 – 21600 

= Rs 55,200

 

Posted by

Rakesh

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