When the digits of the number 14 are reversed, the number increases by 27. How many other two-digitnumbers increase by 27 when their digits are reversed?(a) 5 (b) 6 (c) 7 (d) 8 (e) 9

To solve this problem, we need to find the two-digit numbers that increase by 27 when their digits are reversed.

Let's start by analyzing the given number, 14. When we reverse its digits, we get 41. We can see that 41 - 14 = 27, which satisfies the condition.

Now, let's find other two-digit numbers that also increase by 27 when their digits are reversed. We can start by listing all the two-digit numbers from 10 to 99.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99

Now, let's reverse the digits of each number and check if the difference between the reversed number and the original number is 27.

Reversing the digits of each number, we get:

01, 11, 21, 31, 41, 51, 61, 71, 81, 91, 02, 12, 22, 32, 42, 52, 62, 72, 82, 92, 03, 13, 23, 33, 43, 53, 63, 73, 83, 93, 04, 14, 24, 34, 44, 54, 64, 74, 84, 94, 05, 15, 25, 35, 45, 55, 65, 75, 85, 95, 06, 16, 26, 36, 46, 56, 66, 76, 86, 96, 07, 17, 27, 37, 47, 57, 67, 77, 87, 97, 08, 18, 28, 38, 48, 58, 68, 78, 88, 98, 09, 19, 29, 39, 49, 59, 69, 79, 89, 99

By comparing each reversed number with the original number, we can see that the following numbers have a difference of 27:

14, 41, 25, 52, 36, 63, 47, 74

Therefore, there are a total of 8 two-digit numbers that increase by 27 when their digits are reversed.

The correct answer is (d) 8.