Time and Work. How much work does C do per hour? 
A, B and C need a certain unique time to do a certain work. C needs 1
  hours less than A to complete the work. Working together, they require
  30 minutes to complete 50% of the job. The work also gets completed if
  A and B start working together and A leaves after 1 hour and B works
  for a further 3 hours. How much work does C do per hour? 
(A)16.66% 
(B)33.33% 
(C)50% 
(D)66.66%

My attempt:
Let the total work be 100 units.
Let the work done by A,B and C be a units/hour,b units/hour,c units/hour respectively.
Let the time taken by A alone to complete the work be t hours.
ATQ:
\begin{align*}
(a+b+c) \cdot \frac{1}{2} & =50 \tag{1}\\
(a+b) \cdot 1+b \cdot 3 & =100 \tag{2}\\
c \cdot (t-1)& =100 \tag{3}\\
at & =100 \tag{4}
\end{align*}
Please help me solve these equations. When I am solving it is getting cumbersome. 
Also if someone tells us some other way of solving, that would be helpful as well. Thanks.

Let $A$, $B$ and $C$ be the rates measured in an amount of work per hour $\left(\frac{work}{hour}\right)$ at which workers $A$, $B$ and $C$ accomplish work. If $C$ is the amount of work worker $C$ can do in one hour and $1$ ($100\%$) is the amount of work of the entire job, then $t$ is the time it takes him to bring it to completion: $t=\frac{1}{C}\cdot\frac{\text{work}}{\text{work/hour}}$. We also know that it takes worker $A$ one hour longer to complete the job than it takes worker $C$: $A(t+1)=1 \implies A\left(\frac{1}{C}+1\right)=1$. Another condition that we have is that three of them together require $30$ (or $\frac{1}{2}$ of an hour, don't forget that time is masured in hours here) minutes to complete $50\%$ of the job: $\frac{1}{2}(A+B+C)=\frac{1}{2} \implies (A+B+C)=1$. It is aslo stated that the work also gets completed if worker $A$ and worker $B$ start working together and worker $A$ leaves after $1$ hour and worker $B$ works for a further $3$ hours: $1\cdot(A+B)+3B=1 \implies A+4B=1$. We're all set to go now. Our conditions:
$$
A\left(\frac{1}{C}+1\right)=1\\
A+B+C=1\\
A+4B=1
$$

Solution:

$$
A\cdot\left(\frac{1}{C}+1\right)=1 \implies A=\frac{C}{1+C},\\
A+4B=1 \implies B=\frac{1-A}{4} \implies B=\frac{1}{4(1+C)},\\
A+B+C=1 \implies \frac{C}{1+C}+\frac{1}{4(1+C)}+C=1 \implies C^2+C-1=0 \implies \\
C_{1}=-\frac{3}{2}\text{ (discarded)}\\
C_{2}=\frac{1}{2}=\frac{1\text{ work}}{2\text{ hour}}≡50\%
$$
Answer: $C$ does $50\%$ of work per hour.
