The ratio of present age of P to age of Q four years ago is 2 : 1. Present age of R is equal to average of present age of P and Q. 16 years ago, age of R was 10 years. Find the sum of present age of P , Q and R (in years)?

Correct Answer: 78 years

Let us solve the problem step-by-step by defining variables for the present ages of $P$, $Q$, and $R$.

Let:
$P$ = Present age of P
$Q$ = Present age of Q
$R$ = Present age of R

Step 1: Find the present age of R.
We are given that 16 years ago, the age of R was 10 years.
Therefore, the present age of R is:

$R-16=10$

$R=10+16=26\text{ years}$

Step 2: Find the sum of the present ages of P and Q.
We are given that the present age of R is equal to the average of the present ages of P and Q:

$R=\frac{P+Q}{2}$

Substituting $R=26$ into the equation:

$26=\frac{P+Q}{2}$

$P+Q=26\times 2=52\text{ years}$

Step 3: Calculate the sum of the present ages of P, Q, and R.
We already have:
$P+Q=52$
$R=26$

Now, we find the total sum of their present ages:

$\text{Sum}=P+Q+R$

$\text{Sum}=52+26=78\text{ years}$

Thus, the sum of the present ages of P, Q, and R is 78 years.