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.