Question

P and q do a piece of work in 30 days while q and r do the same work in 24 days and r and p can do it in 20 days.They all work together for 10 days.When q and r leave ,how many more days will p take to finish the work?

Answer 1

Answer:

18 days

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Step-by-step explanation:

1/p + 1/q = 1/30

1/q +1/r = 1/24

1/r + 1/p = 1/20

adding all and dividing by two we get

1/p + 1/q + 1/r = (1/2).(1/30  1/24  + 1/20)

(1/2)(1/120)(4+5+6)

= 1/16

all together can complete work in 16 days

1/p = (1/p + 1/q + 1/r) - (1/q + 1/r)

1/p = 1/16 - 1/24

1/p = (1/48).(3-2)

so p = 48

p needs 48 days to complete work

let say work = w

16 days together required for w

in 10 days work done = 10w/16

remaining work = w- 10w/16

= 6w/16

w work done by p in 48 days

6w/16 work done by p in

(48/w)*(6w/16)

= 18 days