Direction: Read the following information carefully and answer the following questions

In a school consisting of 700 students, a sports event is organized. There are a total of 4 sports i.e Baseball, Cricket, Hockey and Basketball. Each student participated in one sport.

i) Ratio between the number of boys and girls who participated in Cricket is 11 ∶ 13 and that of Hockey is 15 ∶ 13.

(ii) The number of girls who participated in baseball is 20 less than the number of boys and the number of boys who participated in cricket is 35 more than the number of boys who participated in Hockey.

(iii) The ratio between the number of boys and girls who participated in Basketball is 5 ∶ 3

(iv) The ratio of the number of girls and boys who participated in baseball is 7 ∶ 9 and the difference between the number of boys and girls who participated in cricket is 20.

This question was previously asked in

ECGC PO 14 March 2021 Memory Based Test

Option 2 : 12.5%

ECGC PO Full Mock Test

15455

200 Questions
200 Marks
140 Mins

Common explanation:

Ratio between the number of boys and girls who participated in Cricket is 11 ∶ 13 and the difference between the number of boys and girls who participated in cricket is 20

∴ Let the number of boys and girls who participated in cricket be 11x and 13x respectively

⇒ 13x – 11x = 20

⇒ 2x = 20

⇒ x = 10

∴ Number of boys who participated in cricket = 11 × 10 = 110

Number of girls who participated in cricket = 13 × 10 = 130

Ratio between the number of boys and girls who participated in Hockey is 15 ∶ 13 and the number of boys who participated in cricket is 35 more than the number of boys who participated in Hockey.

Let the number of boys and girls who participated in Hockey be 15x and 13x respectively

∴ Number of boys who participated in Hockey = 110 – 35 = 75

⇒ 15x = 75

⇒ x = 5

∴ Number of girls who participated in Hockey = 13 × 5 = 65

The ratio of the number of girls and boys who participated in baseball is 7 ∶ 9 and the number of girls who participated in baseball is 20 less than the number of boys

∴ Let the number of boys and girls who participated in baseball be 9x and 7x respectively

⇒ 9x – 7x = 20

⇒ 2x = 20

⇒ x = 10

∴ Number of boys who participated in baseball = 9 × 10 = 90

Number of girls who participated in baseball = 7 × 10 = 70

Now, the students who took part in Basketball known that there are 700 students in the school

⇒ 700 – (110 + 130 + 75 + 65 + 90 + 70) = 700 – 540 = 160

The ratio between the number of boys and girls who participated in Basketball is 5 ∶ 3

∴ Let the number of boys and girls who participated in basketball be 5x and 3x respectively

⇒ 5x + 3x = 160

⇒ 8x = 160

⇒ x = 20

∴ Number of boys who participated in basketball = 5 × 20 = 100

Number of girls who participated in basketball = 3 × 20 = 60

Following table can be prepared from the above data:

Sports |
Number of Boys |
Number of Girls |

Cricket |
110 |
130 |

Hockey |
75 |
65 |

Baseball |
90 |
70 |

Basketball |
100 |
60 |

Solution:

From the above table:

The total number of children who participated in Hockey = 75 + 65 = 140

The total number of children who participated in Basketball = 100 + 60 = 160

∴ Required percentage = {(160 – 140)/160} × 100 = 12.5%

**∴ The number of children who participated in Hockey is 12.5% less than the number of children who participated in Basketball**