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Question:
A two digit number is obtained by multiplied the sum of digit by 8 and than subtracting 5 or by multiply the difference of digits by 16 and then adding 3. find the number.
Answer:

Let the unit digit and the tenth digit of the number are x and y

So, the number  = 10y + x

Sum of digit = x + y

According to question,

     10y + x = 8(x + y) - 5

=> 10y + x = 8x + 8y - 5

=> 10y + x - 8x - 8y + 5 = 0

=> -7x + 2y + 5 = 0

=> 7x - 2y - 5 = 0

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

Now, difference of the digit = y - x

Again, according to question,

      10y + x = 16(y - x) + 3

=> 10y + x = 16y - 16x + 3

=> 10y + x - 16y + 16x = 3

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

After solving equation1 and 2, we get

x = 3, y = 8

So, the number = 10*8 + 3

                     = 80 + 3

                    = 83

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