A bucket holds somewhere between 100 and150 liters of water. If we fill as many as 3 liters containers we will be left with 1 liter of water, similarly is the case with 4 liters container and 5 liters container then what is the capacity of bucket

Answer 1

So the number must be such that
when divided by 3 , leaves a remainder of 1
when divided by 4 , leaves a remainder of 1
when divided by 5 , leaves a remainder of 1

Find the lowest common number is these sets:

4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64.....

5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 .....

6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 ...

A slow and tedious processs
but did you notice that 61 would work, but it is not between 100 and 150.
However 3x4x5 = 60, so if we add multiples of 60 we have numbers with the given property

So numbers which satisfy the original condition are:
1, 61, 121, 181 , ...
and the one that fits between 100 and 150 is

121

Answer 2

for a fun topic along these lines, Google and look into

the "chinese remainder theorem"