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

Hii friend,

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.

HOPE IT WILL HELP YOU..... :-)

Answer 2

Let the divisor be x


So according to the given condition,

quotient = 6 + 5x

And given that remainder is 1


So now we have,

Dividend = 460
Divisor = x
Quotient = 6 + 5x
and remainder = 1


We know that,

Dividend = Divisor × Quotient + Remainder

=> 460 = x(6 + 5x) + 1

=> 460 = 6x + 5x² + 1

=> 5x² + 6x + 1 = 460

=> 5x² + 6x + 1 - 460 = 0

=> 5x² + 6x - 459 = 0

Now by splitting the middle term,

5x² - 45x + 51x - 459 = 0

=> 5x(x - 9) + 51(x - 9) = 0

=> (x - 9)(5x + 51) = 0

So,

=> (x - 9) = 0/(5x + 51)

=> x - 9 = 0

=> x = 9

If divisor is 9

Then quotient = 6 + 5x

=> Quotient = 6 + 5(9)

=> Quotient = 6 + 45

=> Quotient = 51


Also,

(x - 9)(5x + 51) = 0

=> 5x + 51 = 0/(x - 9)

=> 5x + 51 = 0

=> 5x = -51

=> x = -51/5

If divisor is -51/5

Then quotient = 6 + 5(-51/5)

=> Quotient = 6 - 51

=> Quotient = -45


So your answer :-


For divisor 9 Quotient = 51

For divisor -51/5 Quotient = -45


P.S. :- If you are confused that you can follow only upto the first answer.