Question

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

Answer 1

let the digit at tens place = x
the digit at units place = y
number = 10x + y

According to question :

Case 1 : x + y = 9 ...(1)

Case 2:

9(10x + y) = 2(10y + x)

90x + 9y = 20y + 2x

90x - 2x = 20y - 9y

88x = 11y

8x = y ...(2)

put the value of y in ...(1)

x + 8x = 9

9x = 9

x = 9/9 = 1

put the value of x in ...(2)

8(1) = y

y = 8

the digit at tens place = x = 1

the digit at units place = y = 8

number = 10x + y = 18