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

Answer:

51

Step-by-step explanation:

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.

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