Question

A two digit number is obtained by either multiplying
the sum of digits by 8 and then subtracting 5 or by
multiplying the difference of digits by 16 and adding
3. Find the number.
Ans :
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Answer 1

Let the two digit number be 10x + y where x is the tens digit and y is the ones digit.

Now, according to the question.

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

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

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

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

And,

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

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

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

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

Now, multiplying the equation (1) by 17 and (2) by 7, we get

34x - 119y = - 85 ...............(3)

- 42x + 119y = 21 ..............(4)

Now, adding (3) and (4), we get

34x - 119y = - 85

- 42x + 119y = 21

_________________

- 8x = - 64

_________________

⇒ 8x = 64

x = 64/8

x = 8

So, tens digit is 8.

Substituting the value of x = 8 in (1), we get

2x - 7y = - 5

2*8 - 7y = - 5

16 - 7y = - 5

- 7y = - 5 - 16

- 7y = - 21

7y = 21

y = 21/7

y = 3

=} The required two digit number is 83