Let S represent the price of one shirt in Tk, and let T represent the price of one tie in Tk.

From the given information, we can create two equations:

"Three shirts and five ties cost Tk. 23": 3S + 5T = 23

"Five shirts and one tie cost Tk. 20": 5S + T = 20

Now, we can solve this system of equations using the method of substitution or elimination. Let's use the elimination method:

First, we'll multiply the second equation by 5 to make the coefficients of T in both equations equal:

5(5S + T) = 5(20) 25S + 5T = 100

Now, we have the system of equations:

1. 3S + 5T = 23
2. 25S + 5T = 100

We can subtract equation 1 from equation 2 to eliminate T:

(25S + 5T) - (3S + 5T) = 100 - 23

Simplify:

22S = 77

Now, divide both sides by 22 to find the price of one shirt (S):

S = 77 / 22 S = 3.50

So, the price of one shirt is Tk. 3.50.