Question

P and Q can do one work in 40 days. P alone can do 15 of work in 10 days. in how many days Q alone can complete that work

Answer 1

Given that P and Q together can do a piece of work in 10 days
Work done by P and Q in one day = (1/10)
Given that Q and R together can do a piece of work in 12 days
Work done by Q and R in one day = (1/12)
Given that P and R together can do a piece of work in 15 days
Work done by P and R in one day = (1/15)
2 times work done by (P + Q + R) in one day = (1/10) + (1/12) + (1/15)
On taking LCM of 10, 12, 15 and simplifying, we get
2 times work done by (P + Q + R) in one day = (1/4)
Work done by P, Q and R together in one day = 1/8
P’s work in one day = (1/8) – (1/10) = (1/40)
Hence P can complete the work in 40 days
Q’s work in one day = (1/8) – (1/12) = (1/24)
Hence Q can complete the work in 24 days
R’s work in one day = (1/8) – (1/15) = (7/120)
Hence Q can complete the work in (120/7) days

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Answer 2

ans 600/11 if P can do 1/15 th work in 10 days