Question

On dividing a number by 13 we get 1 as remainder. If the quotient is divided by 5 we get 3 as remainder. If this number is divided by 65 what will be the remainder

Answer 1

let the no. be n

By remainder theorem :-

n=13q+1 -------------1 where q is quotient

also given 

q=5t+3 -------------2 where t is quotient when q is divided by 5

put the value of eq 2 in eq 1 we get

n=65t + 40

Therefore 40 is the remainder

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