Question

The divisor and the quotient of the number6123 are same and the reminder is half the divisor Find the divisor

Answer 1

let divisor of 6123 be x
divisor=quotient given
quotient=x
remainder=x/2
dividend=divisor x quotient+ remainder
6123=x.x+x/2
multiply throughout by 2
2(6123)=2x²+x
12246=2x²+x
2x²+157x-156x-12246=0
x(2x+157)-78(2x+157)=0
(2x+157)(x-78)=0
2x+157=0 or x-78=0
x=-157/2 or x=78
x=-157/2 is not acceptable because divisor cannot be negative
therefore x=78is divisor