P and q complete a work together in 8 days. q and r complete the same work together in 16 days. r and p complete the same work together in 8 days. in how many days p, q and r will complete the work together?
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P and Q complete a work in 8 days
Hence in 1 day they do: 1/8 part of work
Q and R complete the same work in 16 days
Hence in 1 day they do: 1/16 part of work
R and P complete the same work in 8 days
Hence in 1 day they do: 1/8 part of work
In 1 day P&Q,Q&R,R&P do: 1/8 + 1/16 + 1/8 work
2*(P,Q,R) do: 2+1+2/16 work..... [P,Q,R appears 2 times, hence 2*(p.q.r)]
2*(P,Q,R) do 5/16 work in a day
(P,Q,R) do 5/16*2 = 5/32 work in a day
P,Q,R together:
1 day = 5/32 work
X days = 1 work
X = 32/5 days = 6 2/5 days or 6.4 days.
Hence they all together take 6.4 days to complete the work.
Hope it helps
Hence in 1 day they do: 1/8 part of work
Q and R complete the same work in 16 days
Hence in 1 day they do: 1/16 part of work
R and P complete the same work in 8 days
Hence in 1 day they do: 1/8 part of work
In 1 day P&Q,Q&R,R&P do: 1/8 + 1/16 + 1/8 work
2*(P,Q,R) do: 2+1+2/16 work..... [P,Q,R appears 2 times, hence 2*(p.q.r)]
2*(P,Q,R) do 5/16 work in a day
(P,Q,R) do 5/16*2 = 5/32 work in a day
P,Q,R together:
1 day = 5/32 work
X days = 1 work
X = 32/5 days = 6 2/5 days or 6.4 days.
Hence they all together take 6.4 days to complete the work.
Hope it helps
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