The correct option is 60, 84.

Step-by-step Explanation:

Step 1: Understand the given information

We are given that two numbers are in the ratio 5 : 7, and their total sum is 144.

Step 2: Express the numbers using a common variable

Let the common ratio multiplier be $x$.

Therefore, the two numbers can be represented as:

First number = $5x$

Second number = $7x$

Step 3: Set up the equation using their sum

According to the problem statement, the sum of these two numbers is 144.

$5x+7x=144$

Step 4: Solve for $x$

Combine the like terms:

$12x=144$

Divide both sides by 12:

$x=\frac{144}{12}$

$x=12$

Step 5: Calculate the values of the two numbers

Now, substitute $x=12$ back into our expressions for the two numbers:

First number = $5\times 12=60$

Second number = $7\times 12=84$

Thus, the two numbers are 60 and 84.