Question

1, the sum of the digits of a two digit number is 12.if the new number formed by revening the digits is greater than the original by 18. find the number?

plz solve​

Answer 1

$\sf{\huge{\underline{\green{Given :-}}}}$

• The sum of the digits of a two digit number is 12.

• The new number formed by reversing the digits is greater than the original by 18.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The number involved .

$\sf{\huge{\underline{\green{Answer :-}}}}$

Let the number be xy ,

According to the question,

The sum of the digits of a two digit number is 12.

x + y = 12----(1)

• The number = (10x + y)

• Reversing the digits = (10y + x)

The new number formed by reversing the digits is greater than the original by 18.

(10x + y) = (10y + x) + 18

➝ (10y + x) - (10x + y) = 18

➝ 10y + x - 10x - y = 18

➝ 9y - 9x = 18

➝ - (9x - 9y) = 18

➝ 9x - 9y = - 18----(2)

Adding equation 1 & 2

x + y = 12

+9x - 9y = -18

__________

9x + 9y = 108

9x - 9y = -18

_________

18x = 90

________

➝ x = 90/18

➝ x = 5

Putting value in ,(1 )

x + y = 12

➝ 5 + y = 12

➝ y = 12 + 5

➝ y = 7

The number is 57 .