$$\begin{gathered} 0.57 can be written as \\ A. \frac{26}{45} \\ B. \frac{13}{27} \\ c. \frac{13}{29} \\ D. \frac{57}{99} \end{gathered}$$

I think there is some mistake in your question.The number 0.57 must be either

CASE FIRST

If your question has , then the answer is given below.

 Let x = = 0.5777....

⇒ 10x = 5.7777..............  .............(1)

⇒ 100x = 57.7777..........  ..............(2)

subtracting eq.(1) from eq.(2), we get,

 90x = 57.7777..... - 5.7777......

⇒ 90x = 52

so option (a) is correct. 

CASE SECOND 

If your question has , then the answer is given below.

 Let x = =0.57575757.........  ............(1)

⇒ 100x = 57.57575757..............  .............(2)

subtracting eq.(1) from (2), we get,

 99x =57.5757...... - 0.5757.......

⇒ 99x =57

So option (d) is correct in this case.