Question

A number when divided by a divisor leaves 27 as remainder Twice the number when divided by the same number leaves remainder 3.Find the divisor. Please explain.Thanks

Answer 1

Let q1 be quotient of first division and q2 be the quotient of second division, d be the divisor and let original number be num.
The 2 equations formed are:
1) num=d*q1+27
2)2*num=d*q2+3

Multiplying equation-1 by 2 and equating the equations gives us
=>d*q2+3=2dq1+54

Shifting the d term on one side and numbers on the other 
=>d*q2-2*q1=51

Taking d common from the left side
=>d(q2-2q1)=51

=>d=51/q2-2*q1

So d can either be 51 or one of its factor(17 or 3)