Question

I) A number consists of two digits. If the number formed by reversing its digits

is added to it, the sum is 143 and if the same number is subtracted from it the
remainder is 9. Find the number.

Answer 1

Call the two-digit number : ab

The new number formed : ba

We have : 10a + b + 10b + a = 143

11a + 11b = 143

a+b = 143 : 11 = 13

So, we have a few combinations for a and b : (4;9) , (5;8) , (6;7) , (7;6) , (8;5) , (9;4)

Out of all these, only 76 is the satisfied number, as the new number formed is 67, and 76 + 67 = 143 ; 76 - 67 = 9