Question

a student wrote two digits in which the units digits exceeded the tens digits by two. if this number is divided by the sum of its digits, then you get 4 as quotient and 6 as remainder. find out the number written by the student

Answer 1

The easiest way to work this one out is by writing out the possible answers:
13, 24, 35, 46, 57, 68, 79. See, there aren't that many, and you can try applying the rule of Number/(Sum of digits) to each number to find which gives a whole number 4 + a remainder of 6.
So, if you start with 13:
13/(1+3) = 13/4 = 3 with a remainder of 1, as 3x4 = 12 and 12 + 1 = 13.
So the number you're looking for is not 13, but you can continue with the next numbers until you find the right one.