Two numbers are in the ratio 3:5. If 12 is added to both the numbers, then the ratio becomes 5:7. The sum of the given two numbers is

The correct answer is 48.

Let the two given numbers be represented in terms of a constant multiplier $x$.

Since the ratio of the two numbers is given as 3:5, we can write the numbers as:

$\text{First number}=3x$

$\text{Second number}=5x$

According to the problem statement, 12 is added to both numbers, and the new ratio becomes 5:7.

We can set up the equation based on this new ratio:

$\frac{3x+12}{5x+12}=\frac{5}{7}$

Now, cross-multiply to solve for $x$:

$7(3x+12)=5(5x+12)$

$21x+84=25x+60$

Rearrange the terms to isolate $x$:

$84-60=25x-21x$

$24=4x$

$x=\frac{24}{4}$

$x=6$

Now, we need to find the sum of the two original numbers.

$\text{Sum of the numbers}=3x+5x=8x$

Substitute the value of $x=6$ into the equation:

$\text{Sum}=8\×6=48$

Hence, the sum of the given two numbers is 48.