# Question 5db8f

Aug 19, 2017

Parag is $45$ years old.

#### Explanation:

Let's say that $p$ represents Parag's current age and $k$ represents Kalyan's current age.

You know that

p + k = 75" "color(blue)("( * )")#

Now, you also know that Parag is three times as old as Kalyan was when Parag was $k$ years old, Kalyan's current age.

In other words, you can say that $p - k$ represents the number of years that have passed since Parag was as old as Kalyan is now.

This means that Kalyan's age when Parag was three times as old as he was is

$k - \left(p - k\right) = 2 k - p$

Therefore, you can say that you have

$p = 3 \cdot \left(2 k - p\right)$

$p = 6 k - 3 p$

$4 p = 6 k \implies p = \frac{6 k}{4} = \frac{3 k}{2}$

Plug this into equation $\textcolor{b l u e}{\text{( * )}}$ and solve for $k$, Kalyan's current age

$\frac{3 k}{2} + k = 75$

$3 k + 2 k = 150$

$5 k = 150 \implies k = \frac{150}{5} = 30$

Consequently, you will have

$p = 75 - 30 = 45$

Therefore, you can say that Parag is $45$ years old and Kalyan is $30$ years old.

As you can see, Parag is $45$ years old now and Kalyan was $15$ years old when Parag was $30$ years old [Kalyan's current age], so the values check out.