Instructions

Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air. In the flight, sitting is arranged in 30 rows, numbered 1 to 30, each consisting of 6 seats, marked by letters A to F from left to right, respectively. Seats A to C are to the left of the aisle (the passage running from the front of the aircraft to the back), and seats D to F are to the right of the aisle. Seats A and F are by the windows and referred to as Window seats, C and D are by the aisle and are referred to as Aisle seats while B and E are referred to as Middle seats. Seats marked by consecutive letters are called consecutive seats (or seats next to each other). A seat number is a combination of the row number, followed by the letter indicating the position in the row; e.g., 1A is the left window seat in the first row, while 12E is the right middle seat in the 12th row.

Cheap Air charges Rs. 1000 extra for any seats in Rows 1, 12 and 13 as those have extra legroom. For Rows 2- 10, it charges Rs. 300 extra for Window seats and Rs. 500 extra for Aisle seats. For Rows 11 and 14 to 20, it

charges Rs. 200 extra for Window seats and Rs. 400 extra for Aisle seats. All other seats are available at no extra charge.

The following are known:

1. The eight friends were seated in six different rows.

2. They occupied 3 Window seats, 4 Aisle seats and 1 Middle seat.

3. Seven of them had to pay extra amounts, totaling to Rs. 4600, for their choices of seat. One of them did not pay any additional amount for his/her choice of seat.

4. Jayanta, Ajit and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seat. One of these amounts may be zero.

5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.

6. Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of seat. One of these amounts may be zero.

Question 28

Who among the following did not pay any extra amount for his his/her choice of seat?

Solution

We are given that Jayanta, Ajit and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seat.

Let us see how the friends are supposed to pay for the seats they choose:-

In row 1-1000

In row 2-10 - 300 for window and 500 for aisle

In row 11 - 200 for window and 400 for aisle

In row 12,13 - 1000

In row 14-20 - 200 for window and 400 for aisle

In row 21-30 - 0

Thus, As we can see 10, 11 and 12 are the only consecutive seats in which the amounts is different.

Thus, Jayanth, Ajit and Byomkesh sat in row 10, row 11 and row 12.

Manik sat beside Jayantha and thus Manik is also sitting in row 10.

Now we are given that 7 of the 8 friends paid a total of 4600 Rs.

Let's start with the cases:-

It is obvious that 5 friends cannot pay 1000 Rs for their seat because the amount will exceed 4600

Case 1:- 4 friends pay 1000 Rs each. Thus, the remaining friends will pay 600 Rs.

This is possible only when each of them pay 200 Rs.

So the case is- 1000*4 , 200*3

Case 2 :- 3 friends pay 1000 Rs each. Thus, the remaining friends will pay 1600 Rs.

There are 2 cases where this is possible:-

1000*3, 500*2, 400, 200

1000*3, 400*4

Case 3:- 2 friends pay 1000 Rs each. Thus, the remaining 5 friends will pay 2600 Rs.

This is not possible as each friend can pay a maximum of 500 Rs.

Thus, the possible cases are

1000*4 , 200*3

1000*3, 500*2, 400, 200

1000*3, 400*4

As there is no case in which a friend has to pay 300 Rs thus, Jayantha must be sitting in row 10 aisle seat.

Thus, Jayantha paid 500 Rs.

Thus, the case is:-

1000*3, 500*2, 400, 200

Thus, Manik must have also paid 500 sitting in row 10 aisle seat

Ajit must be sitting in row 11 aisle seat paying 400 Rs.

Byomyesh must be sitting row 12 aisle seat paying 1000 Rs.

Thus, among Gargi, Kikira, Pradosh and Tapesh 2 must have paid 1000, 1 must have paid 200 and the remaining person must have paid nothing.

Now we know Gargi and Kikira are sitting adjacent to each other and thus, either both or none of them must have paid 1000 Rs.

Among Pradosh and Tapesh a maximum of 1 person could have paid 1000 Rs.

Thus, the only possible case here is :-

Gargi and Kikira paid 1000 each.

Pradosh is sitting ahead of Tapesh and one of them paid 200 Rs.

Since, both of them were sitting in seats marked by the same letter, in consecutive rows thus, the only possibility is Pradosh sitting in row 20 window seat and paying 200 and Tapesh sitting in row 21 paying nothing.

Thus, the amount paid by each friend is as shown below:-

Tapesh did not paid any amount.

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