A number is divided by 5, 3, 2 successively in order to get remainders of 0, 2, 1 respectively. What will be the remainder when the same number is divided by 2, 3, 5 respectively ?

Let the number = N.
Now N = 5K
K = 3L + 2
L = 2M + 1
K = 3 (2M + 1) + 2
= 6M + 5
N = 5 (6M + 5)
= 30 M + 25.

For M = 0 we get the least number as 25. Now when 25 is divided by 2, we get 12 as quotient and 1 as remainder.
When 12 is divided by 3 we get 4 as quotient, and 0 as remainder. When 4 is divided by 5 we get 4 as remainder.