A mango tree was planted 2 years ago. The rate of its growth is 20% per annum. If at present, the height of the tree is 162 cm, what it was when the tree was planted?

Given,

Present height (P) = 162 cm

R = 20% p.a.

n = 2 years

By formula,

Height before n years = $\dfrac{P}{\Big(1 + \dfrac{r}{100}\Big)^n}$

Substituting the values in formula,

$\text{Height before 2 years }=\dfrac{162}{\Big(1 + \dfrac{20}{100}\Big)^2} \\[1em] = \dfrac{162}{\Big(\dfrac{100 + 20}{100}\Big)^2} \\[1em] = \dfrac{162}{\Big(\dfrac{120}{100}\Big)^2} \\[1em] = \dfrac{162}{\Big(\dfrac{6}{5}\Big)^2} \\[1em] = \dfrac{162}{\dfrac{36}{25}} \\[1em] = \dfrac{162 \times 25}{36} \\[1em] = 112.5$

Hence, the height of the tree when the tree was planted was 112.5 cm.