Question

the sum of a 2 digit number is 11. the number obtained by interchanging the digit exceeds the original number by 27.find the number

Answer 1

Hello!

Maybe this should be the answer.

HOPE IT HELPS!

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 = 11 ............(1) .

The original number = 10x + y .

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

Now,  

⇒ ( 10y + x ) - ( 10x + y ) = 27 .

⇒ 10y + x - 10x - y = 27.

⇒ -9x + 9y = 27.

⇒ 9( -x + y ) = 27.

⇒ -x + y = 27/9 .

⇒ -x + y = 3...........(2) .

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

x + y = 11.

-x + y = 3.

+   -     -

_________

⇒ 2x = 8.

⇒ x = 8/2.

∴ x = 4 .

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

⇒ x + y = 11.

⇒ 4 + y = 11.

⇒ y = 11 - 4 .

∴ y = 7 .

∵ Original number = 10x + y .

= 10 × 4 + 7 .

= 40 + 7 .

= 47 .

Hence, the original number is 47 .

THANKS

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