In the pie chart, half of the fruits in the supermarket are mangoes. The number of pears is $\tfrac{1}{3}$ the number of mangoes.

1. Express the number of mangoes and pears in terms of units

Let the number of mangoes be $3$ units.
Since the number of pears is $\frac{1}{3}$ the number of mangoes, the number of pears is $1$ unit.

2. Find the value of 1 unit using the given difference

Difference in units = $3 \text{ units} - 1 \text{ unit} = 2 \text{ units}$.
We are given that there are $72$ more mangoes than pears.
$2 \text{ units} = 72$
$1 \text{ unit} = 72 \div 2 = 36$

3. Calculate the number of mangoes

Number of mangoes = $3 \text{ units} = 3 \times 36 = 108$