Explanation:

- To find the percentage of students playing cricket, we need to determine how many students are involved in each sport.

- The ratio of cricket to football is 27:13.

- The ratio of football to hockey is 26:14.

- The total number of students is 470.

- First, let's express the ratios with a common reference. The ratio of cricket:football:hockey can be combined using a common intermediate.

- Multiply 27:13 (cricket:football) by 26, and 26:14 (football:hockey) by 13 to equalize the football term.

- Cricket:Football = 27x:13x

- Football:Hockey = 26y:14y

- Equating football counts (13x = 26y): x = 2y

- Substitute:

- Cricket = 27(2y) = 54y

- Football = 13(2y) = 26y

- Hockey = 14y

- Thus, 54y + 26y + 14y = 470

- 94y = 470

- y = 5

- Students playing cricket: 54y = 270

- The percentage of students playing cricket:

- \((270/470) \times 100 = 57.45\%\)

- The given options:

- Option 1: 55.47%

- Option 2: 54.75%

- Option 3: 57.45%

- Option 4: 56.35%

- Correct Answer: Option 3 - 57.45%