Question

P and Q can do a piece of work in 12 days, Q and R in 15 days, R and P in 20 days. In how many days can R alone do it?

• A. 60
• B. 50
• C. 25
• D. 24

Answer 1

The correct option is A 60

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 = 1/12 --------eq1
q + r = 1/15 --------eq2
r + p = 1/20 --------eq3
Adding all the above, 2p + 2q + 2r = 1/12 + 1/15+ 1/20 = 12/60 = 1/5
$p+q+r=1/10$--------eq4
From eq 4 & eq1 --eq4-eq1
$r=1/10-1/12=6-5/60=1/60$
Number of days R needs to work to complete the work =60
Answer (A) 60