Shortcut method
$\rightarrow$ R took $\frac{1}{3}^{rd}$ of the toffees
$\rightarrow$ So total toffees should be perfectly divisible by 3.
$\rightarrow$ From the given options we can see that only 48 is divisible by 3.
$\therefore$ Option C. $48$ is the correct answer.
Detailed method
Start reading from last line and try to go back in time.
If the bowl had $17$ toffees left,how may toffees were originally there in the bowl?
$\rightarrow$ It means now we have $17$ toffees in the bowl.
T took half of the remainder but returned two back into the bowl.
$\bigstar$ returned two back into the bowl.
$\rightarrow$ Out of the $17$ toffees $2$ toffees were given by T .
$\rightarrow$ So if T hadn't returned those $2$ toffees, then there would had been $17-2 =15$ toffees in the bowl.
$\bigstar$ T took half of the remainder
$\rightarrow$ These $15$ toffees are $\frac{1}{2}$ of the remainder which T didn't took and left in the bowl.
$\rightarrow$ So this means we had $15*2=30$ toffees before T took them from the bowl.
S took $\frac{1}{4}^{th}$ of what was left but returned three toffees to the bowl.
$\bigstar$ returned three toffees to the bowl.
$\rightarrow$ Out of the $30$ toffees $3$ toffees were given by S.
$\rightarrow$ So if S hadn't returned those $3$ toffees, then there would had been $30-3=27$ toffees in the bowl.
$\bigstar$ S took $\frac{1}{4}^{th}$ of what was left
$\rightarrow$ These $27$ toffees are $\frac{3}{4}^{th}$ of what was left in the bowl. ($\because$ S took $\frac{1}{4}^{th}$ from the bowl.)
$\rightarrow$ So this means we had $27 * \frac{4}{3} =36$ toffees before S took them from the bowl.
R took $\frac{1}{3}^{rd}$ of the toffees, but returned four to the bowl.
$\bigstar$ returned four to the bowl.
$\rightarrow$ Out of these $36$ toffees $4$ toffees were given by R.
$\rightarrow$ So if R hadn't returned those $4$ toffees,then there would had been $36-4=32$ toffees in the bowl.
$\bigstar$ R took $\frac{1}{3}^{rd}$ of the toffees
$\rightarrow$ These $32$ toffees are $\frac{2}{3}^{rd}$ of what was left in the bowl. ($\because$ R took $\frac{1}{3}^{rd}$ from the bowl.)
$\rightarrow$ So this means we had $32* \frac{3}{2} =48$ toffees before R took them from the bowl.
$\therefore$ $48$ toffees were there in the bowl before any event happened.
So Option C. $48$ is the correct answer.
