Question

A number when divided by 20 gives reminder 15.whereas when the same number is divided by 80, leaves reminder r.find sum of all possible values of r?

Answer 1

let the no be x

x/50=>r=16

x/80=>r=?

Formula:(Divisor*quotient)+remainder=Dividend.

Soln;

now ,

((50*q)+16)=x----->(1)=>now it is the Dividend for the second condition.

so , x/80=r--------->(2)

sub, q=1 r=66

q=2 r=36

q=3 r=6

q=4 r=56

q=5 r=26

q=6 r=76

q=7 r=46

q=8 r=16

q=9 r=66(starts repeated again)

so,n=8.