P can do a job in 8 days, Q in 12 days and R in 16 days. How many days are required to finish the work by R, if he is assisted by P and Q on every second day?

Given:

P can do a job in 8 days, Q in 12 days and R in 16 days.

Concept:

If work is done completely in N days then,

the work done in 1 day will be \(\frac{1}{N}\)

Solution:

According to the question,

P can do a job in 8 days.

Work done by P in 1 day is \(\frac{1}{8}\)

Q can do a job in 12 days

Work done by Q in 1 day is \(\frac{1}{12}\)

R can do a job in 16 days

Work done by R in 1 day is \(\frac{1}{16}\)

Work done by P and Q together is \( \frac{1}{8}+\frac{1}{12}=\frac{15}{72}\)

Since every second day, P and Q are assisting R.

Work done by P, Q, and R together is \( \frac{15}{72}+\frac{1}{16}=\frac{13}{48}\)

Work done in two days will be,

the sum of work done by R in 1 day and work done by P, Q, and R together on the second day. 

\( \frac{13}{48}+\frac{1}{16}=\frac{16}{48}\)

Time taken to complete the work,

\( \frac{48}{16}\times 2=6\)

Hence, option 4 is correct.