Question

The sum of the digits of a two digit number 9.Also nine times this number is twice obtained by reversing the order of the digits. Find the number.

Answer 1

Dear Student,

Let the unit digit and tens digits of the number be x and y

Number = 10y + x

Number after reversing the digits = 10x + y
According to the question,

⇒ x + y = 9 ... (i)

Also,

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

⇒ 88y - 11x = 0

=>11(-x +8y)=0

⇒ -x + 8y =0 ... (ii)

Adding equation (i) and (ii), we get

⇒ 9y = 9

⇒ y = 1 ... (iii)

Putting the value in equation (i), we get

⇒ x = 8

Hence, the number is 10y + x = 10 × 1 + 8 = 18.

Regards