Question

Determine a two digit number whose value is equal to eight times the sum of its digits and when 45 is subracted from the number, the digits are reversed?

Answer 1

Solution:

 

If we consider the digits at the unit's place and at the ten's place be x and y respectively, from the question:

 

the given number, 10 y + x = 8 (x+y)

⇒ 10y + x = 8x + 8y

⇒ 10y - 8y = 8x - x

⇒ y = (7x)/2 - Eq. I

 

Also, from question:

10 y + x - 45 = 10x + y

⇒ 10y-y-45 = 10x-x

⇒ 9y-45 = 9x

⇒ 9y-9x = 45

⇒ y-x = 5 - Eq. II

 

From Eq. I and Eq. II:

 

(7x)/2 - x = 5

⇒ (7x- 2x)/2 = 5

⇒ (7x- 2x) = 5 (2)

⇒ 5x = 5 (2)

⇒ x = 2

 

Substitute x = 2 in Eq. II:

y-2 = 5 or y = 7

 

Thus, the number is 10(7) + 2 = 72.

 

The number is 10(7) + 2 = 72.