Question

The sum of the digits of a two digit-number is 8. When the digits are reversed the number increases by 18 what is the original number

Answer 1

x + y = 8   {equation 1}

The value of xy is 10x + y

The value of yx is 10y + x

10y + x = 10x + y + 18 

9y - 9x = 18

9(y - x) = 18

y - x = 2

From equation 1: y = 8-x

8 - x - x = 2

8 - 2x = 2

-2x = -6

x = 3

y - x = 2

y - 3 = 2

y = 5

Original number xy = 35


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Hope it help u
Mark brainliest

Answer 2

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 .

THANKS

#BeBrainly.