A 2-digit number is such that the sum of the number and the number obtained by reversing the order of the digits of the number is 55. Further, the difference of the given number and the number obtained by reversing the order of the digits of the number is 45. What is the product of the digits?

Shortcut Trick
⇒ 11(x + y) = 55

⇒ x + y = 5 -----(1)

⇒ 9(x - y) = 45

⇒ x - y = 5 -----(2)

From equation (1) and (2)

⇒ x × y = 5 × 0 = 0

∴ The correct answer is 0.

Solution:-

Calculation:

Let 1st digit = x & 2nd digit = y

2-digit number = 10x + y

Reversing the order of the digits of the number = 10y + x

According to question

The sum of the number and the number obtained by reversing the order of the digits of the number = 55

⇒ 10x + y + 10y + x = 55

⇒ 11x + 11y = 55

⇒ x + y = 5 ---------(1)

The difference of the given number and the number obtained by reversing the order of the digits of the number = 45

⇒ 10x + y - 10y - x = 45

⇒ 9x - 9y = 45

⇒ x - y = 5 -----------(2)

Adding Equation (1) & (2)

⇒ x + y + x - y = 10

⇒ 2x = 10 ⇒ x = 5

Put the value of x in equation (1)

⇒ 5 + y = 5 ⇒ y = 0

The product of the digits = 5 × 0 = 0

∴ The correct answer is 0.