Let pbe a two-digit number and qbe the number consisting of same digits written in reverse order. If px 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. The number q, consisting of the same digits written in reverse order, will be 10b + a. Since p and q are two-digit numbers, 'a' and 'b' must be non-zero digits (1-9). We are given that p * q = 2430. To find p and q, we can estimate their values. Since p * q = 2430, p and q should be close to the square root of 2430. sqrt(2430) is approximately 49.29. So, we are looking for two-digit numbers close to 49, whose digits are reversed, and whose product is 2430. Let's test numbers around 49: If p = 45, then its reverse q = 54. Let's check their product: 45 * 54. 45 * 54 = 2430. This matches the given condition (p * q = 2430). So, p = 45 and q = 54 (or vice versa). Now, we need to find the difference between p and q. Difference = |p - q| = |45 - 54| = |-9| = 9. Analyzing the options: A) 45: This would mean |p-q|=45. For example, p=72, q=27. Their product 72*27 = 1944, not 2430. B) 27: This would mean |p-q|=27. For example, p=63, q=36. Their product 63*36 = 2268, not 2430. C) 18: This would mean |p-q|=18. For example, p=54, q=36 (digits not reversed). If p=64, q=46. Their product 64*46 = 2944, not 2430. D) 9: This matches our calculated difference for p=45 and q=54. The final answer is D. The final answer is $\boxed{\text{D}}$