Question

Pavani has a certain number of chocolates; she gave one-third of the chocolates to her brother Arjun, one-sixth to her friend Preeti. She was then left with $30$ chocolates. What is the sum of the number of chocolates did she give to Arjun and Preeti?

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Answer 1

Let the number of chocolates Pavani has be $x$.
$\frac{x}{3}$ are given to Arjun. So now she is left with $x-\frac{x}{3}$ = (2x - 3) chocolates

She gave $\frac{x}{6}$ to Preeti. So, she is left with $\frac{2x}{3}$ - $\frac{x}{6}$ = $\frac{4x}{6}$ - $\frac{x}{6}$ = $\frac{3x}{6}$ = $\frac{x}{2}$
So, $\frac{x}{2}=30$
$x=30\times 2=60$

Initially, Pavani has $60$ chocolates. She gave $\frac{1}{3}$rd i.e. $\frac{60}{3}$ $=20$ to Arjun.
$\frac{1}{6}$th i.e. $10$ chocolates to Preeti.

$\text{Sum = 10 + 20 = 30}$