Question

We get 5/6 when a two digit number is divided by the number with the digits thr difference between the digits is 1 . Find the number.​

Answer 1

Question

We get 5/6 when a two digit number is divided by the number with the digits thr difference between the digits is 1 . Find the number.​

Answer:The original number is 14.

SOLUTION

The sum of the digits of a two-digit number is 5.  

When the digits are reversed, the number formed is 27 more than the

original number.  

Find the original number.

Let x = ones digit

and y = tens digit

from: "The sum of the digits of a two-digit number is 5."

⇒x + y = 5 (equation 1)

from: "When the digits are reversed, the number formed is 27 more than the original number."

⇒10x + y = (10y + x) + 27

⇒9x = 9y + 27

⇒x = y + 3 (equation 2)

Solve equation 1 for y:

⇒x + y = 5

⇒y = 5 - x

Substitute the above into equation 2 and solve for x:

⇒x = y + 3

⇒x = 5 - x + 3

⇒2x = 5 + 3

⇒2x = 8

⇒x = 4 (ones digit)

Substitute the above into equation 1 and solve for y:

⇒x + y = 5

⇒4 + y = 5

⇒y = 5 - 4

⇒y = 1

⇒Solution: The original number is 14.