If 460 is divided by a natural number, quotient is 6 more than 5 times the divisor and remainder is 1 then find quotient and divisor.

Answer

The quotient is 51 and the divisor is 9.

Explanation

Let the divisor be x. Then the quotient is (5x+6) Dividend =divisor `xx` quotient + remainder
`:.460=x(5x+6)+1`
`:.460=5x^(2)+6x+1`
`:.5x^(2)+6x+1=460" ":.5x^(2)+6x+1-460=0`
`:.5x^(2)+6x-459=0" "5x(-459)=5xx(-9)xx51`
`:.x^(2)-45x+51x(x-9)=0" "-45+51` `:.(x-9)(5x+51)=0`
`:.x-9=0or5x+51=0`
`:.x=9or5x=-51`
`x=-(51)/(5)`
But `-(51)/(5)` is not a natural number .
`:.x=-(51)/(5)` is not acceptable.
`:.x=9`
`5x+6=5(9)+6=45+6=51`