# P can do a work in 19 days. Q can in 9.5 days and R can in 28.5 days. Q and R start the work and leave after 3 days...

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P can do a work in 19 days. Q can do the same work in 9.5 days and R can do the same in 28.5 days. Q and R start the work and leave after 3 days. P finishes the remaining work in X days. What is the value of X?

posted Jul 20, 2017

P's speed = 1 work / 19 days
Q's speed = 1 work / 9.5 days
R's speed = 1 work / 28.5 days
Since
Speed × time = work
[((1/9.5)+(1/28.5))×3 + (1/19)×X] = 1
X = 11 Days.

11 days

If W is work then
W=19P=9.5Q=28.5R

Daily speed is:
P=W/19
Q=W/9.5
R=W/28.5

W=3*(W/9.5+W/28.5)+X*W/19
X=11

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