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

Hey dear !!!

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==>>. GIVEN :

Divided = 460

Divided is divided by a natural number

Quotient is 6 more than five times the numerator.

Remainder = 1

Quotient => ? Divisor ==> ?

SOLUTION : Let the divisor be x

According to the question

Quotient = 5x + 6

WE KNOW THAT ,

Divided = Divisor * Quotient + Remainder

Put all the values we get,

460 = x(5x+ 6) + 1

460 = 5x² + 6x + 1

460 - 1 = 5x² + 6x

459 = 5x² + 6x

∴ 5x² + 6x - 459 = 0

By splitting the middle term we get,

5x² + 6x - 459 = 0

5x² + 51x - 45x - 459 = 0

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

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

When,

5x + 51 = 0

5x = -51

x = -51/5

when

x - 9 = 0

x = 9

Here divisor is a natural number hence,
x ≠ -51/5

∴ Divisor = x = 9

∴ Quotient = 5x + 6

∴ Quotient = 5*9 + 6

∴ Quotient = 45 + 6

∴ Quotient = 51

Thanks !!!!!!

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..... :-)