Question

the sum of the digits of a two digit number is 9.also, nine times this number is twice the number obtained by reversing the order of the digits. find the number.

Answer 1

the number is 18. . . ..

Answer 2

Let the digit in the tens place be x.

Let the digit in the ones place be y.

⇒ The number is xy.

The sum of the digits of a two digit number is 9

⇒ x + y = 9

9 times this number is twice the number obtained by reversing the order of the digits

⇒ 9(10x + y) = 2(10y + x)

⇒ 90x + 9y = 20y + 2x

⇒20y - 9y = 90x - 2x

⇒ 11y = 88x

Equations:

║ x + y = 9 -------- (1)

║11y = 88x -------- (2)

From (1)

x + y = 9

x = 9 - y ----------- (Sub into 2)

11y = 88 (9 - y)

11y = 792 - 88y

99y = 792

y= 8 ----------- (Sub into 1)

x + 8 = 9

x = 1

Find the number:

tens place = x = 1

ones place = y = 8

⇒ The number is 18

Answer: 18