Question

Chen writes down a two digit number. He finds that if he
swaps the digits of the number round, the new number he
creates is three more than one third of the original number.
What was the original number?

Answer 1

The original number is 72

Step-by-step explanation:

Let the two digit number be xy.

x is in tenth place and y is in unit place.

The value of the digit = 10x + y

The value of the swapped digit = 10y + x

From question, the new number is three more than one third of the original number.

The new number = 3 + (10x + y)/3

Now,

3 + (10x + y)/3 = 10y + x

9 + 10x + y = 3 × (10y + x)

9 + 10x + y = 30y + 3x

10x + y - 30y - 3x + 9 = 0

7x - 29y + 9 = 0

⇒ 7x - 29y = -9

The value of x and y lies between 0 to 9, on substituting, the only possibility suitable is x = 7 and y = 2.

(7 × 7) - (29 × 2) = -9

49 - 58 = -9

∴ -9 = -9