Question

the sum of two digit number is 10 . the number formed by reversing the digit is 18 less​

Answer 1

ANSWER:-

Let the two digit number be 10x + y where x > y.

Here, x + y = 10    ...(i)

and, 10x + y – 10y – x = 18

⇒  9x – 9y = 18

⇒  9 (x – y) = 18

⇒  x – y = 2   ...(ii)

Solving equations (i) and (ii),

x = 6 and y = 4

∴  Number = 10 × 6 + 4 = 64

• I HOPE IT'S HELPFUL.

Answer 2

Answer:

$GIVEN:-</p><p></p><p>Sum of a two digit no.is 10</p><p></p><p>The number is reversed and the new number formed is 18 less than Original Number.</p><p></p><p>Now,</p><p></p><p>\implies{Ones\:digit\:be=x}⟹Onesdigitbe=x</p><p></p><p>\implies{Tens\:digit=(10-x)}⟹Tensdigit=(10−x)</p><p></p><p>\implies{Original\:number=x+10(10-x)=100-9x}⟹Originalnumber=x+10(10−x)=100−9x</p><p></p><p>Again,</p><p></p><p>Atq</p><p></p><p>After reversing the digit,</p><p></p><p>\implies{Ones\:digit=(10-x)}⟹Onesdigit=(10−x)</p><p></p><p>\implies{Tens\:digit=x}⟹Tensdigit=x</p><p></p><p>\implies{New\:Number=10-x+10(x)}⟹NewNumber=10−x+10(x)</p><p></p><p>\implies{New\:Number=9x+10}⟹NewNumber=9x+10</p><p></p><p>Now,</p><p></p><p>(New Number)-(Original Number)=18.</p><p></p><p>(9x+10)-(100-9x)=18(9x+10)−(100−9x)=18</p><p></p><p>9x+10-100+9x=189x+10−100+9x=18</p><p></p><p>18x-90=10818x−90=108</p><p></p><p>18x=10818x=108</p><p></p><p>x=\frac{108}{18}x=18108</p><p></p><p>x=6x=6</p><p></p><p>Hence,</p><p></p><p>Original Number is 64.</p><p>$