the sum of the digit of a two digit number is 8. if the number formed by reversing the digits is less than original number by 18.F

1 thought on “the sum of the digit of a two digit number is 8. if the number formed by reversing the digits is less than original number by 18.F”

1. Given

   Sum of the digit of a two digit number is 8

   Number obtained by reversing the digits is less than the original number by 18.

   To Find

   We have to find the original number.

   [tex]\sf\huge\bold{\underline{\underline{{Solution}}}}[/tex]

   Let the digits be ‘x’ and y where x is at unit place and y is at tens place

   The number formed is : 10y +x

   Number obtained Through reversing the order of digits : 10x+y

   According to the question

   Reversed number is less than the original number by 18

   ➾10y+x-(10x+y)=18

   ➾10y+x-10x-y=18

   ➾9y-9x=18

   ➾9(y-x)=18

   ➾y-x=2————–(1)

   Also,the sum of its digits is 8

   So, x+y=8———–(2)

   Adding Equation 1 and 2

   ➾y-x+x+y=2+8

   ➾2y=10

   ➾y=5

   put y’s value in Equation 2

   ➾x+y=8

   ➾x+5=8

   ➾x=8-5=3

   x=3

   Let’s finding the number

   Original number :10y+x= 10(5)+3=53

   Obtained by reversing the digits:10x+y=30+5=35

   Reply