Question

The sum of the digits in a two-digit number
is 7. If we add 9 to the number, the digits are
interchanged. Find the number.​

Answer 1

Answer:x + y = 7.............(1) .

The original number = 10x + y .

Number obtained on reversing the digits = 10y + x .

Now,  

⇒ 10y + x = 10x + y + 9 .

⇒ 10x - x  + y - 10y = -9.

⇒ 9x - 9y = -9.

⇒ 9( x - y ) = -9.

⇒ x -y = -9/9 .

⇒ x - y = -1...........(2) .

On substracting equation (1) and (2), we get

x + y = 7.

x - y = -1.  

-   +     +

_________

⇒ 2y = 8.

⇒ y = 8/2.

∴ y = 4 .

On putting the value of y in equation (1), we get  

⇒ x + y = 7.

⇒ x + 4 = 7.

⇒ x = 7 - 4 .

∴ x = 3 .

∵ Original number = 10x + y .

= 10 × 3 + 4 .

= 30 + 4 .

= 34 .

Hence, the original number is 35 .