## Finding Percentage Increase and Decrease

#### Formulas for Percentage Increase and Decrease:

Percentage increase

=

× 100%

Percentage decrease

=

× 100%

=

amount increased |

initial quantity |

Percentage decrease

=

amount decreased |

initial quantity |

There are 10 children in each group below.

2 more children join Group A.

The number of children in Group A increases by 2.

Percentage increase =

× 100%

= 20%

There are now 20% more children in Group A than before.

2 more children join Group A.

The number of children in Group A increases by 2.

Percentage increase =

2 |

10 |

= 20%

There are now 20% more children in Group A than before.

3 children from Group B leave the group.

The number of children in Group B decreases by 3.

Percentage decrease =

× 100%

= 30%

There are now 30% fewer children in Group B than before.

The number of children in Group B decreases by 3.

Percentage decrease =

3 |

10 |

= 30%

There are now 30% fewer children in Group B than before.

####
Word Problem 1: Lisa's salary was raised from $4000 to $4800 per month. What was the percentage increase in her monthly salary?

Percentage increase =

× 100%

= 20%

The percentage increase in her monthly salary was 20%.

$800 |

$4000 |

= 20%

The percentage increase in her monthly salary was 20%.

####
Word Problem 2: The price of a chair was reduced from $270 to $189 in a sale. Find the percentage discount on the chair.

Decrease in price = $270 − $189

= $81

Percentage decrease =

× 100%

= 30%

The percentage discount on the chair was 30%.

= $81

Percentage decrease =

$81 |

$270 |

= 30%

The percentage discount on the chair was 30%.

####
Word Problem 3: Joey had a leaky water bottle that leaked 15 ml of water every 10 minutes. What was the percentage decrease in the water in the bottle 1 hour after the bottle was filled up to 450 ml?

10 minutes → 15 ml

1 minute →

ml

60 minutes →

ml × 60

= 90 ml

After 1 hour 90 ml of water had leaked from the bottle.

Percentage decrease =

× 100%

= 20%

The percentage decrease in the water after 1 hour was 20%.

1 minute →

15 |

10 |

60 minutes →

15 |

10 |

= 90 ml

After 1 hour 90 ml of water had leaked from the bottle.

Percentage decrease =

90 |

450 |

= 20%

The percentage decrease in the water after 1 hour was 20%.

####
Word Problem 4: Due to some roadworks on the usual route from home to school, Peggy has to take another route to school which is 7% longer. This increase in distance is 126 m. What is the length of the new route?

7% → 126 m

1% →

m

= 18 m

107% → 18 m × 107

= 1926 m

The length of the new route is 1926 m.

1% →

126 |

7 |

= 18 m

107% → 18 m × 107

= 1926 m

The length of the new route is 1926 m.

####
Word Problem 5: Sue bought a piece of cloth 140 cm long. After washing it, the cloth shrank by 4% along its length. What is the length of the cloth now?

100% − 4% = 96%

96% of 140 cm =

× 140 cm

= 134.4 cm

The length of the cloth is 134.4 cm now.

96% of 140 cm =

96 |

100 |

= 134.4 cm

The length of the cloth is 134.4 cm now.