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×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:
- 27×90 (90 is not the reverse of 27)
- 30×81 (81 is not the reverse of 30)
- 45×54 (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.