If 3 times Mary’s present age is 20 years more than 5 times Diya's present age, and 2 times Diya's present age is 2 years less than Mary's present age, then what is the difference (in years) between the ages of Mary and Dia?

The correct option is 16.

Let us break down the problem step-by-step to find the present ages of Mary and Diya.

Let Mary's present age be $M$ years and Diya's present age be $D$ years.

From the first given condition: "3 times Mary’s present age is 20 years more than 5 times Diya's present age."

We can write this as an equation:

$3M=5D+20$    — (Equation 1)

From the second given condition: "2 times Diya's present age is 2 years less than Mary's present age."

We can express this as another equation:

$2D=M-2$

Rearranging this to express $M$ in terms of $D$:

$M=2D+2$    — (Equation 2)

Now, substitute the value of $M$ from Equation 2 into Equation 1:

$3(2D+2)=5D+20$

Expand the left side of the equation:

$6D+6=5D+20$

Subtract $5D$ and $6$ from both sides:

$6D-5D=20-6$

$D=14$

So, Diya's present age is 14 years.

Now, substitute $D=14$ back into Equation 2 to find Mary's present age:

$M=2\left(14\right)+2$

$M=28+2$

$M=30$

So, Mary's present age is 30 years.

Finally, we need to find the difference between the ages of Mary and Diya:

$\text{Difference}=M-D$

$\text{Difference}=30-14=16$

The difference between the ages of Mary and Diya is 16 years.