Question

the sum of the digits of a 2-digits number is 8.the number obtained interchange the digits exceeds the given number by 18. find the given numbers.

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 .  

⇒ 10y + x - 10x - y = 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. +   -     - _________  

⇒ 2x = 6.  

⇒ x = 6/2.  

∴ x = 3 .  

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

⇒ x + y = 8.  

⇒ 3 + y = 8.  

⇒ y = 8 - 3 .  

∴ y = 5 .  

∵ Original number = 10x + y .

 = 10 × 3 + 5 .  

= 30 + 5 .

 = 35 .  

Hence, the original number is 35 .  

THANKS  

#BeBrainly.

Answer 2

Hi there !
Here's the answer:

•°•°•°•°•°•<><><<><>><><>•°•°•°•°•°

¶¶¶ SOLUTION :

In a two digit No.,
Let units digit be x
& tens digit be (8-x)
(°•° Given that sum of two digits = 8)

•°• The No. is given by
No. = 10 × (face value of tens place) + 1 × (face value of units place)
=>Original No. = 10(8-x) + x

Now,
The digits are interchanged
New No. = 10(x) + (8-x)

Given,
New No. - Original No. = 18

=> 10x+(8-x) - [10(8-x)+x] = 18
=> 10x+8-x - 80 +10x-x = 18
=> 20x-2x -72 = 18
=> 18x = 90
=> x = 5

•°• Units digit of original 2-digit No. = x = 5
& Tens digit of original 2-digit No. = 8-x = 8-5 = 3.

•°• Required 2-digit No. = 35

•°•°•°•°•°•<><><<><>><><>•°•°•°•°•°

¶¶¶ VERIFICATION:

No. = 35
Sum of digits = 8

-- Interchange of digits --
New No. = 53

53 - 35 = 18

•°• Given Data Matched.

•°•°•°•°•°•<><><<><>><><>•°•°•°•°•°

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:)

Hope it helps