A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

Let ten's place digit of a two digit number is x and unit's place digit is y.

So, two digit number = 10 x + y

According to condition 1

10x + y = 8 (x + y) - 5

=> 2x - 7y = - 5 ... (1)

According to condition 2

10x + y = 16 (x - y) + 3

=> 6x - 17y = - 3 ... (2)

On solving equation (1) and (2) we get

x = 8 and y = 3

So, two digit number is 10x + y = 10 * 8 + 3 = 83.