Engineer P can assemble a software module in 20 hours, while Engineer Q can complete the same module independently in 30 hours. P and Q collaborate on the task for 6 hours, after which Engineer R takes over and replaces them both. If R completes 40% of the remaining work, what percentage of the total assembly work was performed by R?

Correct Answer: 20%

Step-by-Step Explanation:

Step 1: Calculate the work rates of Engineer P and Engineer Q
Let the total software module assembly work be equal to 1 unit.

Engineer P takes 20 hours to finish the module independently. Therefore, P's work rate per hour is:
$\text{P's rate}=\frac{1}{20}$

Engineer Q takes 30 hours to finish the module independently. Therefore, Q's work rate per hour is:
$\text{Q's rate}=\frac{1}{30}$

Step 2: Calculate the work completed by P and Q together in 6 hours
The combined rate of work when P and Q collaborate is:
$\text{Combined rate}=\frac{1}{20}+\frac{1}{30}=\frac{3+2}{60}=\frac{5}{60}=\frac{1}{12}$

Since they work together for 6 hours, the fraction of total work completed by P and Q is:
$\text{Work done by P and Q}=6\times \frac{1}{12}=\frac{6}{12}=\frac{1}{2}$
Thus, P and Q complete 50% of the total work.

Step 3: Calculate the remaining work
After P and Q work for 6 hours, the remaining portion of work is:
$\text{Remaining work}=1-\frac{1}{2}=\frac{1}{2}$
In terms of percentage, 50% of the total work remains to be completed.

Step 4: Calculate the percentage of work done by Engineer R
Engineer R takes over and completes 40% of the remaining work.
$\text{Work done by R}=40\%\times 50\%=0.40\times 50\%=20\%$

Hence, Engineer R performed 20% of the total assembly work.