Question

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

Answer 1

Let the Divisor be X.
Then the Quotient = 5X+6
Dividend = 460
Remainder = 1
We know that,
Dividend = Divisor × Quotient + Remainder
460 = X × (5X+6) + 1
460 = 5X²+6X+1
5X²+6X-459 = 0
5X²+51X-45X-459 = 0
X(5X+51)-9(5X+51) = 0
(X-45) (5X+51)= 0
(X-9)= 0 OR(5X-51) = 0
(X-9) = 0
X = 9
Divisor = X = 9
And,
Quotient = 5X +6 = 5 × 9 + 6 = 51.