Question

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

Answer 1

Dividend = 6123
Now, divisor and quotient are same
Let divisor = quotient = d

Now, remainder = `1/2xxx=x/2`

Since dividend = divisor * quotient + remainder, we have

`6123= d^2+d/2`

∴12246= 2d²+d

∴2d²+d-12246 = 0

Comparing with ax²+bx+c, we get

a= 2, b= 1, c=-12246

`therefore d=(-b+-sqrt(b^2-4ac))/(2a)`

`=(-1+-sqrt(1^2-4(2)(-12246)))/4`

`=(-1+-sqrt97969)/4`

`=(-1+-313)/4`

∴`d=(-1+313)/4 or d=(-1-313)/4`

∴d= 78 or d= -78.5

Ignoring the negative value, the divisor is 78.