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?
1.5
2.6
3.8
4.9​

Answer 1

Answer:

There are five ( 5 ) other pairs like that

Step-by-step explanation:

Let's assume the digit as xy

In decimal system, the number is expressed as 10*x + y

Then it's reverse expression is 10*y + x

The difference between these two expressions is given as 27

Therefore, ( 10*y + x ) - ( 10*x + y) = 27

10*y + x - 10*x - y = 27

10*y - y -10*x + x = 27

9*y - 9*x = 27

9*(y - x) = 27

y - x = 27/9

y - x = 3

y = x+3

By Substituting the value of 'x' with natural numbers (1,2,3,4....)

If x =1, y = 1+3=4 i.e., the required pair is 14 & 41

If x =2, y = 2+3=5 i.e., the required pair is 25 & 52

If x =3, y = 3+3=6 i.e., the required pair is 36 & 63

If x =4, y = 4+3=7 i.e., the required pair is 47 & 74

If x =5, y = 5+3=8 i.e., the required pair is 58 & 85

If x =6, y = 6+3=9 i.e., the required pair is 69 & 96

After excluding the pair 14 & 41, there are 5 such possible pairs.

Answer 2

There are 6 no. And they are

14

25

36

47

58

69