In Class 8 of a school, the ratio of students playing cricket to those playing football is 27 : 13, while the ratio of those playing
football to those playing hockey is 26 : 14. If the total number of students in Class 8 is 470, and each student plays exactly one
game, find the percentage of students of the class playing cricket. [Give your answer correct to two decimal places.]
This questions was previously asked in
SSC CHSL 25th May 2022 Shift-2
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%
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By: santosh