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 the total work be 1, or 100%.
Let the efficiency of A,B and C be a,b and c(percentage of work be done in an hour)

(1) $\frac{1}{c}$ + 1 = $\frac{1}{a}$

(2) $(a+b+c)\cdot\frac{1}{2}$ = $\frac{1}{2}$
(3) $(a+b)\cdot1 + b\cdot3 = 1$

from (3) you get

a + 4b = 1
b = $\frac{1-a}{4}$

put it into (2)

a + $\frac{1-a}{4}$ + c = 1
4a + 1 - a + 4c = 4
a = $\frac{3-4c}{3}$

put it into (1)
$\frac{1}{c} + 1 = \frac{3}{3-4c}$
$\frac{1+c}{c} = \frac{3}{3-4c}$
$4c^2 + 4c - 3 = 0$
$4c^2 + 4c + 1 = 4$
$(2c + 1)^2 = 4$
2c + 1 = 2 (c can not be negative)
c = 0.5
The final answer is C 50%.
