Rajesh, in his printing press, got an order to print some books, out of which be completed $\frac{17}{27}$ of the order in 34 days. In how many days did he completed the entire order of printings?

The correct answer is 54.

Let the total printing order be represented as 1 unit (or the entire order).
We are given that Rajesh completes $\frac{17}{27}$ of the order in 34 days.

To find the time taken to complete the entire order (which is 1 unit), we can use the unitary method.
Let $x$ be the total number of days required to complete the entire order.

The rate of work done per day is constant, so we can set up the proportion:
$\frac{\text{Work done}}{\text{Days taken}}=\text{Constant rate}$

Therefore, we write:
$\frac{\left(\frac{17}{27}\right)}{34}=\frac{1}{x}$

Now, we solve for $x$ by cross-multiplying:
$x=34\times \frac{27}{17}$

We can simplify this by dividing 34 by 17:
$\frac{34}{17}=2$

Substituting this back into the equation gives:
$x=2\times 27$
$x=54$

Thus, Rajesh will complete the entire order of printings in 54 days.