Question

A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are reversed, find the number?

Answer 1

Hey there !!

Let the ten's digit of the original number be x .

And, the unit's digit of the original number be y.

Now, A/Q

⇒ x + y = 8 ............(1) .

The original number = 10x + y .

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

Now,  

⇒ 10y + x = 10x + y + 18 .

⇒ 10x - x  + y - 10y = -18.

⇒ 9x - 9y = -18.

⇒ 9( x - y ) = -18.

⇒ x -y = -18/9 .

⇒ x - y = -2...........(2) .

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

x + y = 8.

x - y = -2.  

-   +     +

_________

⇒ 2y = 10.

⇒ y = 10/2.

∴ y = 5 .

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

⇒ x + y = 8.

⇒ x + 5 = 8.

⇒ x = 8 - 5 .

∴ x = 3 .

∵ Original number = 10x + y .

= 10 × 3 + 5 .

= 30 + 5 .

= 35 .

Hence, the original number is 35 .

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