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.
the number​

Answer 1

The sum of the digits of a 2 digit number is 8.

Let the digits at 1s place be x. Then, the digits at 10s place is (8 - x)

Therefore original number = 10 (8 - x) + x

80 - 10x + x

80 - 9x

On interchanging the digits from 1s to 10s and vice versa

New number obtained = 10x + 8 - x

= 9x + 8

According to the statement, the number obtained by interchanging the digits exceed the original number by 18. The number to find out.

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 digit at 1s place is 5.

Now, digits at 10s place = (8 - 5) = 3.

Thus, the original number is 35 and the new number after interchanging the places of digits is 53.

Answer the original number is 35 and the new number is 53

Answer 2

Answer:

35

Step-by-step explanation:

Let ones digit = x

Tens digit = 8 - x

No. = 10(8-x) + x = 80 - 10x + x = 80 - 9x

AFTER CHANGING

Ones digit = 8 - x

Tens digit = x

No. = 10x + 8 - x = 9x + 8

A.T.Q

9x + 8 - 80 + 9x = 18

18x - 72 = 18

18x = 18 + 72

18x = 90

x = 5

NO. = 35