Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p x q…
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?
45
27
18
9
Solution
The product 2430 ends in 0, so one of the digits must be 5. Let the other digit be x, so p = 10x + 5 and q = 50 + x. Then $(10x + 5)(50 + x) = 2430$ leads to $2x^2 + 101x - 436 = 0$, giving $x = 4$. So p = 45 and q = 54, and the difference is $54 - 45 = 9$.