Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p x q = 2430, then what is the difference between p and q?

Let the two-digit number p be represented as 10a + b, where 'a' is the tens digit and 'b' is the units digit. Then, the number q, formed by reversing the digits, will be 10b + a. We are given that p x q = 2430. (10a + b)(10b + a) = 2430. To find p and q, we can estimate their values. Since their product is 2430, p and q must be close to the square root of 2430. The square root of 2430 is approximately 49.29. Let's test two-digit numbers around this value that are reverses of each other. Consider p = 45. Then q (with digits reversed) would be 54. Let's check their product: 45 x 54 = 2430. This matches the given condition p x q = 2430. So, the two numbers are 45 and 54. The question asks for the difference between p and q. Difference = |54 - 45| = 9. Analyzing the options: A) 45: This is one of the numbers, not the difference. B) 27: This is not the difference between 45 and 54. C) 18: This is not the difference between 45 and 54. D) 9: This is the correct difference between 45 and 54. The final answer is D.