The ratio of two numbers is 5 : 7 and their sum is 96. Find the numbers.

The correct option is 40, 56.

Let's solve the problem step-by-step to find the two numbers.

We are given that the ratio of the two numbers is 5 : 7.
Let the common ratio multiplier be x.
Therefore, the two numbers can be represented as $5x$ and $7x$.

According to the problem statement, the sum of these two numbers is 96. We can set up the following equation:

$5x+7x=96$

Combining the like terms on the left side of the equation:

$12x=96$

Now, solve for x by dividing both sides by 12:

$x=\frac{96}{12}$

$x=8$

Now that we have found the value of x, we can find the actual values of the two numbers:

First number = $5x=5\times 8=40$

Second number = $7x=7\times 8=56$

Thus, the two numbers are 40 and 56.