Question

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

Answer 1

Let, Divisor be x

According to the question,

• Quotient = 5x + 6

• Remainder = 1

• Dividend = 460

Dividend = Divisor × Quotient + Remainder

460 = x(5x + 6) + 1

⇒ 460 = 5x² + 6x + 1

⇒ 460 - 1 = 5x² + 6x

⇒ 459 = 5x² + 6x

⇒ 5x² + 6x - 459 = 0

On factorizing the equation,

5x² + 51x - 45x - 459 = 0

⇒ x(5x + 51) - 9(5x + 51) = 0

⇒ (x - 9)(5x + 51) = 0

Now we have;

x - 9 = 0              OR                 5x + 51 = 0

→ x = 0 + 9          OR             → 5x = -51

→ x = 9                 OR             → x = -51 ÷ 5

It is given that x is a natural number.

∴ Divisor = x = 9

⟶ Verification:

Dividend = Divisor × Quotient + Remainder

⇒ 460 = 9(51) + 1

⇒ 460 = 460

★ Hence Verified ★