When a two-digit number is multiplied by the sum of its digits, the product is 424. When the number obtained by interchanging its digits is multiplied by the sum of the digits, the result is 280. The sum of the digits of the given number is:

When a two-digit number is multiplied by the sum of its digits, the product is 424. When the number obtained by interchanging its digits is multiplied by the sum of the digits, the result is 280. The sum of the digits of the given number is: Correct Answer 8

Let the unit digit number be x and tens digit number be y, then number is 10y + x

According to the question

(10y + x) × (x + y) = 424      ----(1)

(10x + y) × (x + y) = 280      ----(2)

Divide equation (1) by (2)

⇒ (10y + x)/(10x + y) = 424/280

⇒ (10y + x)/(10x + y) = 53/35

We can write

(10y + x)/(10x + y) = (50 + 3)/(30 + 5) (or we can find the value of x and y after solving in detail).

∴ x = 3 and y = 5