Question

A number consists of two digits whose product is 18. If 27 is added to the number, the digits
interehange their places. Find the number.​

Answer 1

Answer:

36

Step-by-step explanation:

Let the unit digit be 'y' and the tens digit be 'x'.  Thus, the number be 10x + y.

Product of digit = xy = 18  ⇒ x = 18/y

If 27 is added to the number, the digits interchange their places. And the new number becomes 10y + x.

⇒ (10x + y) + 27 = 10y + x

⇒ 27 = 9y - 9x

⇒ 3 = y - x

⇒ 3 = y - (18/y)        {from above}

⇒ 3y = y² - 18

⇒ y² - 3y - 18 = 0

⇒ y² - 6y + 3y - 18 = 0

⇒ (y + 3)(y - 6) = 0

  As y can't be -ve, y = 6.

Thus , x = 18/y = 18/6 = 3

∴ Required number = xy = 36

Answer 2

Answer:

Question :-

• A number consists of two digits whose product is 18. If 27 is added to the number, the digits Interchange their place.

Find out :-

• Find the number.

Let the number be 10x + y

Given that,

➻ xy = 18 . . . . . (i)

also,

➻ 10x + y + 27 = 10y + x

➻10x - x + y + 27 = 10y

➻9x + 27 = 10y - y

➻9x + 27 = 9y

➻9(x + 3) = 9y

➻(x + 3) = 9y/9

➻(x + 3) = y

➻x + 3 = y ...(ii)

➠ using (ii) in (i) get

➻x(x + 3) = 18

➻x² + 3x = 18

➻x² + 3x - 18 = 0

➻ x² + (6 -3)x - 18 = 0

➻x² + 6x - 3x - 18 = 0

➻x(x + 6) - 3(x + 6) = 0

➻(x + 6) (x - 3) = 0

➻ x + 6 = 0

➙x = -6

or,

➻x - 3 = 0

➙x = 3

x can't be negetive.

Hence,

➔y = x + 3

➔y = 3 + 3

➔y = 6

❖ So, required number is ,

➭ 10x + y

➭ 10(3) + 6

➭ 30 + 6

➪ 36

Henceforth, the number is 36.