Question

In the two digit number the digit in unit place is equal to square of digit in tens place . If 54 is added to the digit the digits get interchanged . Find the numbers

Answer 1

Step-by-step explanation:

Let the tens digit = x, and the units digit =y.

Then y = x^2 .

The original number is then 10x + x^2.

When 54 is added the new number is 10y + x (digits reversed).

Therefore 10x + x^2 + 54 = 10x^2 + x

10x^2 + x - x^2 - 10x - 54 = 0

9x^2 - 9x - 54 = 0

x^2 - x - 6 = 0 (divide throughout by 9)

(x - 3)(x + 2) = 0

Therefore x-3 = 0 or x + 2 = 0.

Therefore x = 3

Therefore y = x^2 = 9

Therefore the original number = 10x + y = 39.

Answer 2

Step-by-step explanation:

In the two digit number the digit in unit place is equal to square of digit in tens place . If 54 is added to the digit the digits get interchanged . Find the numbers