Question

The sum of the digits of a two-digit number is 9. The number is 6 times the unit digit. Find the number.


please correct answer today is my exam​

Answer 1

Answer:

The required two digit number is 36.

Step-by-step-explanation:

Let the digit at tens place be x.

And the digit at units place be y.

∴ The two-digit number = xy = 10x + y

From the first condition,

x + y = 9

⇒ x = 9 - y

⇒ x = - y + 9 - - - ( 1 )

From the second condition,

10x + y = 6y

⇒ 10x = 6y - y

⇒ 10x = 5y

⇒ 10 ( - y + 9 ) = 5y - - - [ From ( 1 ) ]

⇒ - 10y + 90 = 5y

⇒ 90 = 5y + 10y

⇒ 15y = 90

⇒ y = 90 ÷ 15

⇒ y = 6

∴ The unit digit = 6

By substituting y = 6 in equation ( 1 ), we get,

x = - y + 9

⇒ x = - 6 + 9

⇒ x = 3

∴ The tens digit = 3

Now,

The two-digit number = 10x + y

⇒ The two-digit number = 10 * 3 + 6

⇒ The two-digit number = 30 + 6

⇒ The two-digit number = 36

∴ The required two digit number is 36.