Question

The sum of the digits of a 2-digit number is 8. The number obtained by
interchanging the digits exceeds the given number by 18. Find the given numbers.​

Answer 1

Answer:

Step-by-step explanation:

Let the digits at ones place be x. Then,

the digits at tens place = (8-x)

Original number = 10(8-x) + x

= 80 - 10x + x

= 80 - 9x

On interchanging the digits

new number obtained = 10x + 8-x

= 9x + 8

According to question,

New number - Original number = 18

9x + 8 - (80-9x) = 18

=> 9x + 8 - 80 + 9x = 18

=> 18x - 72 = 18

=> 18x = 18 + 72

=> 18x = 90

=> x = 90/18

=> x = 5

Hence, the digits at ones place is 5.

The digits at tens place = (8-5) = 3.

So, the original number is 35 and the new number is 53.

Answer 2

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⏩Let the digits at ones place be x. Then, the digits at tens place = (8 - x)

Original number = 10 (8 - x) + x

= 80 - 10x + x

= 80 - 9x

On interchanging the digits..

new number obtained = 10x + 8 - x

= 9x + 8

According to question,

New number - Original number = 18

9x + 8 - (80-9x) = 18

=> 9x + 8 - 80 + 9x = 18

=> 18x - 72 = 18

=> 18x = 18 + 72

=> 18x = 90

=> x = 90/18

=> x = 5

Hence, the digits at ones place is 5.

The digits at tens place = (8 - 5) = 3.

So, the original number is 35 and the new number is 53.

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