Question

A number when successively divided by 3,5 and 8 leaves remainder 1,4 and 7 respectively. Find the respective remainders if the order of divisors be reversed?

Answer 1

Let number is N
N = 3P + 1
P = 5Q + 4
Q = 8R + 7

So,
P = 40R + 39
N = 120R + 157
N = 120R + 152 + 5
N = 8(15R + 19) + 5

Thus remainder is 5 when divided by 8.

Now (15R + 19) is divided by 5
So, 15R + 19 = 15R + 15 + 4 = 5(3R + 3) + 4

Thus remainder is 4.

Now (3R + 3) is divided by 3
3R + 3 = 3(R + 1)

Thus remainder is 0 as it is multiple of 3.

Answer
5, 4, 0