Question

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.Find the original number​

Answer 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.

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

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