Question

Sum of the digits of a two-digit number is 8.When we interchange the digits, it is found that the resulting new number is less than the original number by 54.
What is the two-digit number?.​

Answer 1

Step-by-step explanation:

Solution:-

Let the tens digit of the number be x

As, the Sum of two- digits is 8

So, the unit digit be (8 - x)

The original number = 10x + (8 - x) = 9x + 8

The number obtained by interchanging the digits

= 10(8 - x) + x

= 80 - 10x + x

= 80 - 9x

The interchanged number is less than the original number by 54

$\sf \dashrightarrow9x + 8 - (80 - 9x) = 54$

$\sf \dashrightarrow9x + 8 - 80 + 9x = 54$

$\sf \dashrightarrow18x - 72= 54$

$\sf \dashrightarrow18x = 54 + 72$

$\sf \dashrightarrow18x = 126$

$\sf \dashrightarrow x = \dfrac{126}{18} = 7$

The tens digit is 7

The units digit = 8 - x = 8 - 7 = 1

The original number = 10(7) + 1 = 71

∴ The original number = 71

Answer 2

Step-by-step explanation:

Solution :-

Let the tens digit of the number be x

As, the Sum of two- digits is 8

So, the unit digit be (8 - x)

The original number = 10x + (8 - x) = 9x + 8

The number obtained by interchanging the digits

= 10 (8 - x) + x

= 80 - 10x + x

= 80 - 9x

The interchanged number is less than the original number by 54

⇢$9x+8−(80−9x)=54$

⇢$9x+8−80+9x=54$

⇢$18x−72=54$

⇢$18x=54+72$

⇢$18x=126$

⇢$= \dfrac{126}{18} =7$

The tens digit is 7

The units digit = 8 - x = 8 - 7 = 1

The original number = 10 (7) + 1 = 71

∴ The original number = 71