Question

The sum of the digits of a two-digit number is 13 and the difference between the number and that formed by reversing the digits is 27. What is the product of the digits of the number?
1. 35
2. 40
3. 45
4. 54

Answer 1

Correct Answer - Option 2 : 40

Given:

The sum of the digits of a two-digit number = 13

The difference between the number and that formed by reversing the digits = 27

Calculation:

Let the digit in the 10th place and unit place are a and b respectively.

So, the two-digit number is 10a + b.

According to the question,

a + b = 13      ----(1)

Again, according to the question,

(10b + a) - (10a + b) = 27

⇒ 10b + a - 10a - b = 27

⇒ 9b - 9a = 27

⇒ 9(a - b) = 27

⇒ a - b = 3      ----(2)

By adding equ(1) and equ(2), we get

(a + b) + (a - b) = 13 + 3

⇒ 2a = 16

⇒ a = 8

From equ(1), b = 13 - a

⇒ 13 - 8

⇒ 5

Now, the product of the digits = 8 × 5

⇒ 40

∴ The product of the digits of the number is 40.