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

Correct Option (4)

Let the two-digit number p be represented as $10a+b$, where 'a' is the tens digit and 'b' is the units digit. Consequently, the number q, formed by reversing the digits of p, is $10b+a$.

The problem states that $p\times q=2430$.

To identify p and q, we examine two-digit factor pairs of 2430 where one number is the reverse of the other. The relevant two-digit factor pairs of 2430 include:

• $27\times 90$ (90 is not the reverse of 27)
• $30\times 81$ (81 is not the reverse of 30)
• $45\times 54$ (54 is the reverse of 45)

Thus, the numbers satisfying the condition are $p=45$ and $q=54$ (or vice versa). The required difference between p and q is $|54-45|=9$.

Incorrect Options:

The calculated difference between p and q is 9.

• The value 45 represents one of the numbers, p or q, not their difference. This option is incorrect because it does not represent the difference.
• The value 27 is a factor of 2430, but it does not correspond to the difference between p and q as determined by the problem's conditions.
• The value 18 is not the result obtained from calculating the difference between p and q based on the given product and digit reversal condition.