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 diviser

Answer 1

Using Remainder theorem:

460 = Divisor x Quotient + Remainder

Let divisor be D, quotient be Q, and Remainder is given 1

So,

460 = Q.D + 1

Q.D = 459.....(1)

Now we have,

Q = 5D + 6....(2)

Solving (1) and (2) we get

Q = 459/D

Putting this in (2) we get

459/D = 5D + 6

459 = 5D² + 6D

5D² + 6D -459 = 0

5D² - 45D + 51D -459 = 0

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

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

D = 9 or -51/5

As it is given that divisor is natural number, D will only be 9

Divisor = 9
Quotient = 459/9 = 51

Answer 2

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..... :-)