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 in
11’s, no chair will be left.
(i) In the hall, how many chairs are available?
(a) 407 (b) 143
(c) 539 (d) 209
Answers
Answer:
Total Number of Chairs in Hall = 539
Step-by-step explanation:
The Condition and Situation are that he has such an amount of Chairs available, that if he arranges them in groups of 2,3,4,5, and 6, he is left with 1, 2, 3, 4, and 5 Chairs respectively.
One Easy and good way is to check it with the Options!
1 ) Divide the options with numbers 2 to 6, and see if they leave a remainder (the answer of division) between 1 to 5 respectively!
2 ) Along with this, there is also the condition that, if the Chairs are arranged in groups of 11, no chairs are left, meaning it is such a number, that when divided by 11, leaves no remainder. Now, here, for us, there is no number, that does not leave a remainder of 0, after being divided by 11.
3 ) Going through the options as such,
- Option A (407) is Divisible by all the said numbers (2, 3, 4, 6, 11) leaving behind the respective amount, but it is not divisible by 5. (not leaving behind the remainder of 4.)
- Option B (143) is Divisible by all the said numbers (2, 3, 4, 6, 11) leaving behind the respective amount, but it is not divisible by 5. (not leaving behind the remainder of 4.)
- Option C (539) is Divisible by all the said numbers (2, 3, 4, 5, 6, 11) leaving behind the respective amount.
- Option D (209) is Divisible by all the said numbers (2, 3, 5, 6, 11) leaving behind the respective amount, but it is not Possible by 4 (not leaving behind the remainder of 3).
I hope this Explanation was Adequate. I Apologise if you did not understand even after reading this far, please do tell me how I can Improve here, or you can ask me about the answer in the comments. Have a Good day!
Answer:
539
Step-by-step explanation: