The sum of digits of a two-digit number is 14 and the difference between the two digits of the number is 2. The product of the two digits of the number is:

48

The correct answer is Option (3) → 48

1. Define the Variables

Let the two digits of the number be $x$ and $y$.

2. Set Up the Equations

• Sum of the digits: $x + y = 14$
• Difference between the digits: $|x - y| = 2$

We can solve this using the two possible scenarios for the difference:

Case 1: $x - y = 2$

Adding the two equations:

$(x + y) + (x - y) = 14 + 2$

$2x = 16$

$x = 8$

Now, substitute $x = 8$ back into the first equation:

$8 + y = 14$

$y = 6$

Case 2: $y - x = 2$

Following the same logic, we would find that $y = 8$ and $x = 6$.

In both cases, the two digits of the number are 6 and 8. (The number is either 68 or 86).

3. Calculate the Product

The question asks for the product of these two digits:

$\text{Product} = 6 \times 8 = 48$

Conclusion

The product of the two digits of the number is 48.