P, Q and R can complete a work in 10 days, 20 days and 30 days, respectively, working alone. - SSC STUDY

P, Q and R can complete a work in 10 days, 20 days and 30 days, respectively, working alone. How soon can the work be completed if P is assisted by Q and R on alternate days?

Options:
a) 7 days
b) 9 days
c) 5 days
d) 6 days

Solution

As per question
L.C.M. = 10 , 20 , 30 =60
Efficiency of P = $\frac{60}{10}$ = 6
Efficiency of Q = $\frac{60}{20}$ = 3
Efficiency of R = $\frac{60}{30}$ = 2
P and Q complete work = 6 + 3 = 9
P and R complete work = 6 + 2 = 8
In 2 days complete work = 9 + 8 = 17
In 6 days complete work = (17 x 3) = 51
Remain work = 60 – 51 = 9
In 7 days = 9

Ans: b) 9 days