Question

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

Answer 1

ANSWER :-

• Divisor = 9
• Quotient = 51

GIVEN :-

• 460 is divided by a natural number , quotient is 6 more than 5 times the divisor and remainder is 1.

TO FIND :-

• Quotient and Divisor.

TO KNOW :-

★ Natural numbers are 1 , 2 , 3 , 4 .. and so on.

★ Dividend = (Quotient × Divisor) + Remainder

SOLUTION :-

Let the Divisor be 'd'.

Quotient is 6 more than 5 times the divisor.

Hence , Quotient will be '6 + 5d'.

We have , Dividend = 460

ㅤㅤㅤㅤㅤRemainder = 1

We know ,

Dividend = (Quotient × Divisor) + Remainder

Putting values we get..

→ 460 = [ (6 + 5d)(d) ] + 1

→ 460 - 1 = 6d + 5d²

→ 459 = 6d + 5d²

→ -5d² - 6d + 459 = 0

Multiplying whole equation by ( - ),

→ 5d² + 6d - 459 = 0

Now we will solve this quadratic equation by splitting middle term.

→ 5d² + 51d - 45d - 459 = 0

→ d(5d + 51) - 9(5d + 51) = 0

→ (d - 9) (5d + 51) = 0

→ (d - 9) = 0 or (5d + 51) = 0

→ d = 9 or → d = -51/5

But Divisor = d = Natural number

So, it can't be negative.

Hence , d = 9.

♦ Divisor = d = 9

♦ Quotient = 6 + 5d = 6 + 5(9) = 51

Hence , Divisor is 9 and Quotient is 51.

VERIFICATION :-

Dividend = 460

Remainder = 1

Divisor = 9

Quotient = 51

Putting values in formula...

460 = (51)(9) + 1

460 = 459 + 1

460 = 460 (verified)