Question

The square of the sum of the digits of a two digit number is 64 . if 3 is added to four times the number, the digits are reversed. find the number​

Answer 1

Step-by-step explanation:

Doesn't appear to be possible as 64 cannot be expressed as the sum of squares of 2 digits.

If we re- phrase the question as “ The square of the sum of the digits of a two digit number is 64. If 3 is added to 4 times the number, its digits get reversed. What is the number ?”, it will be possible to find a solution.

Let the two - digit number be 10 x + y

Then, as per the question, (x + y)^2 = 64

So, x + y = 8 ….(1)

Also, 4(10 x +y) + 3 = 10 y + x …. ( digits reversed)

Or, 40 x + 4 y + 3 = 10 y + x

Or, 40 x - x = 10 y - 4 y - 3

Or, 39 x = 6 y - 3

Or, 6 y = 39 x + 3

Or, y = (39 x + 3) / 6 = 3 (13x + 1) / 6 = (13 x + 1) / 2

Substituting this value of y in (1) above, we have:

x + (13 x + 1) /2 = 8

Or, 2 x + 13 x + 1 = 16

Or, 15 x = 16 -1 = 15

So, x = 1

From (1) above, y = 8 - 1 = 7

So the number is (10*1) + 7 = 17 Answer.

Check:

Square of the sum of digits of 17 = (1 + 7)^2 = 8^2 =64✓

4 times the number = 4 * 17 = 68

If we add 3 to 68, we get 71. So, the digits of the original number 17 get reversed.✓