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?

Correct option is D

Given:

Reversing the digits of 14 gives 41, and 41 - 14 = 27.
We need to find how many other two-digit numbers behave the same way — i.e., their reversed digits result in an increase of 27.

Concept Used:
Let the two-digit number be 10a + b, where a is the tens digit and b is the units digit.
Its reversed form is 10b + a.
Solution:

10b + a - (10a + b) = 27

10b + a - 10a - b = 27

9b - 9a = 27

b - a = 3

So we are looking for two-digit numbers where units digit − tens digit = 3.

Possible values of a: 1 to 6
Then corresponding numbers:

a = 1, b = 4  $$\rightarrow$$ 14

a = 2, b = 5 $$\rightarrow$$ 25

a = 3, b = 6 $$\rightarrow$$ 36

a = 4, b = 7 $$\rightarrow$$ 47

a = 5, b = 8 $$\rightarrow$$ 58

a = 6, b = 9 $$\rightarrow$$ 69

Total numbers = 6
Excluding 14 (already given), we have:

5 other numbers