Let's denote:

• The cost of 1 shirt as "S" in Tk.
• The cost of 1 pair of trousers as "T" in Tk.
• The cost of 1 hat as "H" in Tk.

Now, you're given two sets of purchases:

The cost of 5 shirts, 5 pairs of trousers, and 3 hats is Tk. 710, which can be expressed as: 5S + 5T + 3H = 710

The cost of 11 shirts, 11 pairs of trousers, and 8 hats is Tk. 1590, which can be expressed as: 11S + 11T + 8H = 1590

Now, we need to solve this system of equations to find the values of S, T, and H:

Let's simplify the equations by dividing both sides of each equation by the number of items to find the cost of 1 of each item:

(5S + 5T + 3H) / 5 = 710 / 5 S + T + (3/5)H = 142

(11S + 11T + 8H) / 11 = 1590 / 11 S + T + (8/11)H = 144.55 (approximately)

Now, we have two equations:

S + T + (3/5)H = 142

S + T + (8/11)H = 144.55

Subtract the first equation from the second equation to eliminate S and T:

(S + T + (8/11)H) - (S + T + (3/5)H) = 144.55 - 142

Now, simplify:

(8/11)H - (3/5)H = 2.55

To add or subtract fractions, we need a common denominator. In this case, it's 55:

(40/55)H - (33/55)H = 2.55

(7/55)H = 2.55

Now, solve for H:

H = (2.55 * 55) / 7 H ≈ 20

Now that we know the cost of 1 hat (H) is approximately Tk. 20, we can find the cost of 1 shirt and 1 pair of trousers using the original equation:

5S + 5T + 3H = 710

5S + 5T + 3(20) = 710

5S + 5T + 60 = 710

5S + 5T = 710 - 60

5S + 5T = 650

Now, divide both sides by 5 to find the cost of 1 shirt and 1 pair of trousers:

S + T = 650 / 5

S + T = 130

So, the total cost of 1 shirt, 1 pair of trousers, and 1 hat is S + T + H = 130 + 20 = Tk. 150.