Question

When you reverse the digits of the number 14 the number increases by 27. How many other two digit numbers increase by 27 when their digits are reversed?

Answer 1

Answer:

25, 47, 58, 69.

Step-by-step explanation:

Let us assume the number is 10x+7, then on the reversal of the digits x and y we get a new number, 10y+x.

Now, the difference between those two numbers is 27 always.

Hence, we can write, (10y+x)-(10x+y) =27

⇒9y -9x =27

⇒ y-x =3 ...... (1)

So, putting x= 1,2,3,4,5,6,7,8,9, ..... in the equation (1), we get y=4,5,6,7,8,9,10,11,12, .....respectively. Since the numbers are of two digits, so, y≠ 10,11,12 or more.

Hence, (x,y) =(1,4), (2,5), (3,6), (4,7), (5,8), and (6,9).

Therefore, the other numbers are 25,47,58,69. (Answer)