Determine the fraction of people who drank mango juice.

Let the total number of people be $T$.
Fraction of people who drank mango juice $= \frac{3}{8}$.

Remainder $= 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}$ of the total people.

Fraction of people who drank pineapple juice $= \frac{1}{4}$ of the remainder. $= \frac{1}{4} \times \frac{5}{8} = \frac{5}{32}$ of the total people.

The rest drank orange juice.
Fraction of people who drank orange juice $= \text{Remainder} - \text{Fraction for pineapple juice}$

To subtract these fractions, find a common denominator, which is 32.

So, the fraction for orange juice $= \frac{20}{32} - \frac{5}{32} = \frac{15}{32}$ of the total people.

We are given that 240 people drank orange juice.

To find $T$, multiply 240 by the reciprocal of $\frac{15}{32}$:

So, there were 512 people in total at the ceremony.

Number of people who drank mango juice $= \frac{3}{8}$ of the total people.

The number of people who drank mango juice is 192.