Three numbers are in the ratio of 2:5:6 and their sum is 663. Find the three numbers:

The correct option is 102, 255, 306.

To find the three numbers, we can follow these step-by-step logical and mathematical calculations:

Step 1: Understand the ratio
The three numbers are in the ratio of 2:5:6. This means we can represent the three numbers as:
First number = $2x$
Second number = $5x$
Third number = $6x$
where $x$ is a common multiplier (or constant of proportionality).

Step 2: Set up the equation using the sum
We are given that the sum of these three numbers is 663. Therefore, we can write the equation:
$2x+5x+6x=663$

Step 3: Solve for $x$
Combine the like terms on the left side of the equation:
$(2+5+6)x=663$
$13x=663$
Now, divide both sides by 13 to find the value of $x$:
$x=\frac{663}{13}$
$x=51$

Step 4: Calculate the three numbers
Now substitute the value of $x=51$ back into our original expressions for the three numbers:
First number = $2\times 51=102$
Second number = $5\times 51=255$
Third number = $6\times 51=306$

Thus, the three numbers are 102, 255, and 306, which matches the correct option.