P, Q and R can do a piece of work in 100, 75 and 25 days respectively. P is assisted by Q on one day and R on the next day alternatively. How long would the work take to finish ?

27\(\frac{3}{11}\) days

( P + Q )'s 1 day work = 3 + 4 = 7

( Q + R )'s 1 day work = 3 + 12 = 15

2 days work = 15 + 7 = 22 unit

2 days  ------- 22 unit

but total work to be done is 300 unit so  multiply 22 by \(\frac{150}{11}\)

similarly number of days = 2 × \(\frac{150}{11}\) 

= 27\(\frac{3}{11}\) days