Atwo-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.