1. Successive Percentage Changes

2. Successive Percentage Changes
Consider the following tree which was originally 2 m high.
After the first year, its height has increased by 2%,
and after
the second year, its height has further increased by 5%.
How high is the tree after two years?
Increased by 5% ?
Increased by 2%
2 m
After the 1st year
After the 2nd year
This question involves successive percentage changes.

3. From the previous page,
the height of the tree after one year =
2  (1 + 2%) m
= 2  1.02 m
= 2.04 m
the height of the tree after two years =
2.04  (1 + 5%) m
= 2.04  1.05 m
= m
Or we can simply write…
the height of the tree after two years
= 2  (1 + 2%)  (1 + 5%) m
= 2  1.02  1.05 m
= m

4. Follow-up question
1. The price of a toy car was $200 in In 2009 and 2010, the price was increased by 10% and 20% respectively. Find the price of the toy car in 2010.
Solution
The price of the toy car in 2010
20%) (1
10%)
$200 + × =
1.2
1.1
$200 × =
$264 =

5. Follow-up question (cont’d)
2. Mary’s weight is 40 kg now. If her weight was decreased by 3% 2 years ago and then further decreased by 4% last year, find her weight 2 years ago. (Give your answer correct to 2 decimal places.)
Solution
Let x kg be Mary’s weight 2 years ago. 40
4%) (1
3%) = - × x
0.96
0.97 40 = x
d.p.) 2 to
(cor.
42.96 =
∴ Mary’s weight was kg 2 years ago.