In a two-digit number, if it is known that its ten's digit exceeds its unit's digit by 2 and that the product of the given number and the sum of its digits is equal to 252 then the number is:

Let the number be 10a + b where a is tens digit and b is units digit. Given a = b + 2. Also (10a + b)(a + b) = 252. Substituting a = b + 2: (10(b+2) + b)((b+2) + b) = 252, which simplifies to (11b + 20)(2b + 2) = 252. Testing b = 2 gives (42)(6) = 252, so the number is 42, which matches the condition that tens digit (4) exceeds units digit (2) by 2.