p and q can weave a mat in 12 days ,q and r together do it 15 days ,if p is twice as good a workman as R,find in what time Q will do it alone?
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Answer:
20 days
Step-by-step explanation:
Given,
p and q can weave a mat in 12 days
P+Q=1/12 ----(1)
q and r together do it 15 days
Q+R=1/15 ----(2)
by subtracting (1)-(2)
P-R=1/12-1/15-----(3)
if p is twice as good a workman as R
P=2R
P/R=2/1 efficiency
time is reciprocal of Efficiency
P/R=1x/2x
P=1/x
R=1/2x
P-R=1/x-1/2x ----(4)
by Equating Eq(3) and (4)
1/12-1/15=1/x-1/2x
5-4/60=2x-x/x*2x
1/60=x/2x*x
x=30
P is 1/x=1/30 days
R is 1/2x=1/60 days
From Eq(2)
Q=1/15-1/60
Q=4-1/60
Q=3/60
Q=1/20 days
Q can do a piece of work in 20 days
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