⟩ There are few items which we have to put items in boxes. if 3 items put in each box, 1 item left outside. if 4 items put in each box, 1 item left outside. if 5 items put in each box, 1 item left outside. if 6 items put in each box, 1 item left outside. if 7 items put in each box, 0 item left outside. How many number of item are there?
Answer is 301..
3 - 100 boxes - 1 left
4 - 75 boxes - 1 left
5 - 60 boxes - 1 left
6 - 50 boxes - 1 left
7 - 43 boxes - 0 left
Solution:
3,4,5,6 - 1 left & 7 - 0 left - (ie) - least common multiple
of 3,4,5,6 + 1 which is divisible by 7.
the least common multiples are: 60,120,180,240,300
61 - not divisible by 7
121 - not divisible by 7
181 - not divisible by 7
241 - not divisible by 7
301 - divisible by 7
hence 301 is the answer
