Question

A number consists of two digits. The ten's digit i8 2/3 times of unit's digit. If the digits are reversed, the
number is increased by 27. Determine the number.
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Answer 1

Answer:

The number can be written in the form 10*x + y, where y is the unit digit and x is the 10’s digit.

For instance: 38 is 3*10 + 8, and x=3 and y=8.

Reversing the order of digits, we get 10*y + x.

We know that the number plus the number obtained by reversing the digits is 121.

Or 10x + y + 10y + x = 121.

Or 11x + 11y = 121

We also know that the digits differ by 3. So, x - y = 3 (It could also be y - x = 3)

Multiplying this equation by 11, we get 11x - 11y = 33.

Adding the two equations, we get:

11x + 11y + 11x - 11y = 121 + 33.

or 22x = 154 or x = 7 and therefore y = x -3 = 4.

Therefore the number is 74.

Remember that we could also have y -x =3, in which case the number is 47, which gives us the same result.