Question

when you reverse the digits of the number 14, the number increase by 27. How manyother two digitsnumbers increase by 27 when their digits are reversed?

Answer 1

Answer:

4

Step-by-step explanation:

14, 25, 36, 47, and 58 increase by 27 when your reverse their digits.

Answer 2

Answer:

There are 5 such numbers.

To Find:

The digits which when reversed increased by 27

Solution:

Let the two-digit nunber = xy = 10x + y

When digit are reversed = yx = 10y + x

Their difference should be 27

⟹ (10y + x) - ( 10x + y ) = 27

⟹ 10y + x - 10x - y = 27

⟹ 9y - 9x = 27

⟹ 9 ( y - x ) = 27

⟹ y - x = 27/9

⟹ y - x = 3

The difference between x and y should be 3

The numbers satisfy this condition:

• 1 and 4 ⟹ 14
• 2 and 5 ⟹ 25
• 3 and 6 ⟹ 36
• 4 and 7 ⟹ 47
• 5 and 8 ⟹ 58
• 6 and 9 ⟹ 69

Total numbers = 6

Total numbers except 14 = 5