Question

Mahesh works as a manager in a hotel. He has to arrange seats in hall for a function. A hall has a certain number of chairs. Guests want to sit in different groups like in pairs, triplets,quadruplets, fives and sixes etc. When Mahesh arranges chairs in such pattern like in 2’s,3’s, 4’s 5’s and 6’s then 1, 2, 3, 4 and 5 chairs are left respectively. But when he arranges in11’s, no chair will be left.

Q)If one chair is removed, which arrangements are possible now?

1)2

2)3

3)4

4)5

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Answer 1

Given : When Mahesh arranges chairs in such pattern like in 2’s,3’s, 4’s 5’s and 6’s then 1, 2, 3, 4 and 5 chairs are left respectively. But when he arranges in11’s, no chair will be left.

To Find :  Minimum number of Chairs

If one chair is removed, which arrangements are possible now

Solution:

Chairs  = C

C  = 2M + 1  => C  + 1 =  2(M + 1)

C  = 3N + 2  => (C + 1) = 3(N + 1)

C = 4O  + 3 => C + 1 = 4(O + 1)

C = 5P + 4   => C + 1 = 5(P + 1)

C = 6Q + 5  =>  C + 1  = 6(Q + 1)

C = 11R

Hence LCM of 2 , 3 , 4 , 5 , 6 must a factor of  C+1

LCM of  2 , 3 , 4 , 5 , 6

= 60

C+ 1 = 60K

C = 11R

=> 11R = 60K  -  1

=>  k =9   , R = 49

Chairs  = 539

If one chair is removed,

538

is Divisible by 2

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