In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is Tk. 560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is Tk. 1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?

Let, x be the price of one shirt,

y be the price of one pair of trousers and z be the price of one hat.

According to the question,

4x + 4y + 2z = 560……….(i)

9x + 9y + 6z = 1, 290………(ii)

3x + 3y + 2z = 430……………….(ii)              [Divide all terms of equation (ii) by 3]

Now, we have [(i)-(iii))]

$$\begin{gathered} \frac{4x + 4y + 2z = 560....................\left(i\right) \\ 3x + 3y + 2z = 430...................\left(iii\right)}{\therefore x + y = 130......................\left(iv\right)} \\ Again, from equation \left(iii\right) \\ 3x + 3y + 2z = 430 \\ = 3(x + y) + 2z = 430 \\ Putting value from equation \left(iv\right)] \\ 3 \times 130 + 2z = 430 \\ \therefore z = 20 \\ \therefore x + y + z = 130 + 20 = 150 ans. \end{gathered}$$