P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?  Choose the correct option:
A) 4 B) 8 C) 12 D) 16 E) 18
Let work done by P in 1 day = p   work done by Q in 1 day =q   Work done by R in 1 day = r   p + q = 1/8 ---(1)   q + r= 1/12 ---(2)   p+ q+ r = 1/6 ---(3)   (3) – (2) =&gt; p = 1/6 - 1/12 = 1/12   (3) – (1) =&gt; r = 1/6 – 1/8 = 1/24   p + r = 1/12 + 1/24 = 3/24 = 1/8   =&gt; P and R will finish the work in 8 days   Answer is 8.
<result>B</result>
P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?