SOLUTION: p&q can do a piece of work in 10 days, q&R in 12 days while p&R can do it in 12 days .in how many days p alone can do the work

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Question 815711: p&q can do a piece of work in 10 days, q&R in 12 days while p&R can do it in 12 days .in how many days p alone can do the work

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
p&q can do a piece of work in 10 days, q&R in 12 days
while p&R can do it in 12 days, in how many days p alone can do the work
:
let the completed job = 1
:
"p&q can do a piece of work in 10 days,"
10%2Fp + 10%2Fq = 1
:
q&R in 12 days
12%2Fq + 12%2Fr = 1
:
while p&R can do it in 12 days
12%2Fp + 12%2Fr = 1
:
in how many days p alone can do the work
we know that
12%2Fq + 12%2Fr = 12%2Fp + 12%2Fr
if we subtract 12/r from both sides
12%2Fq = 12%2Fp
therefore: q = p
Replace q with p in the 1st equation
10%2Fp + 10%2Fp = 1
20%2Fp = 1
p = 20 days for p to do it alone