The sum of the digits of two-digit number is 7. If the digits are reversed, the number is decreased by 27. What is the original number?

hope this helps you

have a nice day

Step-by-step explanation:

Answer

Let the original number be

yx

; i.e., 10y+x. We know x+y=7. The number obtained by reversing the digits in

xy

, i.e., 10x+y. The second condition gives 10x+y−2=2(10y+x). Thus we have two equations:

x+y=7(1)

8x−19y=2(2)

Multiply the equation (1) by 19 and get

19x+19y=133.

Adding this to (2), we obtain 27x=135. This gives x=5. Hence y=7−x=7−5=2.

The required number is 25.