### Important Formulas to solve racing problems

#### Some Terms used in the questions:

statements | mathematical interpretations |
---|---|

A beats B by t seconds | A finishes the race t seconds before B finishes. |

A gives B a start of t seconds | A starts t seconds after B starts from the same starting point. |

A gives B a start of x metres | While A starts from the starting point, B starts x meters ahead from the same starting point at the same time.
To cover a race of 100 metres in this case, A will have to cover 100 metres while B will have to cover only (100 – x) metres. |

Game of 100 | A game in which the participant who scores 100 points first wins. |

In a game of 100, A can give B 20 points | While A scores 100 points, B scores only 100-20=80 points. |

#### 1.In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

Correct!
Wrong!

#### 2. In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:

Correct!
Wrong!

#### 3.In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

Correct!
Wrong!

#### 4.In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:

Correct!
Wrong!

#### 5. In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:

Correct!
Wrong!

QUIZ ON RACES AND GAMES

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