Amitabh has a certain number of toffees, such that if
he distributes them amongst ten children he has nine
left, if he distributes amongst 9 children he would
have 8 left, if he distributes amongst 8 children he
would have 7 left … and so on until if he distributes
amongst 5 children he should have 4 left. What is
the second lowest number of toffees he could have
with him?
I get that there is a pattern like 10-9=1. 9-8=1 etc. but I'm not able to put pen to paper and solve it iskei aage kya karna hai
Please log in to comment and participate in discussions.
Academic discussion and doubt solving for: HCF & LCM, Integral Solutions, Divisibility Rules, Factorisation, Unit Digit, Remainders.
Create an account to join our community and participate in discussions.
For these questions just take the LCM. To understand the concept, here's an example. Distributing 4 at once, I have 3 toffees left. Distributing 5 at once, I have 4 left. Think of it this way, if I had 1 more toffee then the number would be perfectly divisible by 5 and 4, thus LCM of 5 and 4 which is 20. But this is if I had one more, thus 20-1 = 19. You can check, 19/5 = 4 left and 19/4 = 3 left.
Similarly for this question, it started at 10 and ended at 5. Thus, I'll take LCM of 5,6,7,8,9 and 10 which is 2520. Number of toffees are in form of 2520K - 1.
Smallest number of toffees will be at K = 1 ie 2519. Second smallest will be at 5039 which should be the answer.
Okay thanks