Question

find the least number which leaves a remainder 5 when divided by 9 and a remainder 1 when divided by 17

Answer 1

let the no be x
x = 9q + 5. ..............,..eqn 1
x = 17q + 1...................eqn2
from 1 and 2 we have
9q + 5 = 17q + 1
5 - 1 = 17q - 9q
4. = 8q
q. = 1 / 2

putting q = 1 / 2 in eqn 1 we get
x = 9× 1/2. +. 5
= 9/2. +. 5
= 9.5