Question

the sum of the digits of a two-digit number is 8.if the digit are reversed,the new number increases by 18.find the number.

Answer 1

Let the original number be 10x + y and the new number formed by interchanging of digits becomes 10y + x. It is said that sum of digits of the two digit number is 8.

So, y + x = 8 .....(1)

Then, it is also said that the new number is greater than the original number by 18. So, equation formed is :

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

10 y + x - 10x - y = 18

9y - 9x = 18

y - x = 2 ( taking 9 to be common ) ....(2)

Adding equation (1) and (2),

y + x + y - x = 8 + 2

2y = 10

Hence, y = 5

Using (1) we get, x = 8 - y = 8 - 5 = 3

So, the number is 10x + y = 35

Thus, 35 is the original number.