A number when divided by a certain divisor leaves a remahyder
5. Also 8 times the number and 12 times the number when
divided by the same divisor leaves remainders 6 and 9
respectively. The divisor is
Answers
Answered by
3
5. 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)
Since,
We have a reminder of 27 in one case d cannot be less than 27
So ,
divisor is 51
Similar questions