P and Q can do a piece of work in 12 days,Q and R can do a piece of work in 18 days and R and P can do piece of work in 15 days.in how many days R alone can do the same work?
Answers
Step-by-step explanation:
Given,
★P and Q can do a piece of work in 12days.
★Q and R can do a piece of work in 18 days.
★R and P can do a piece of work in 15days.
To Find :-
In how many days R alone can do the work .
Solution:-
Let,
the work done by P = P days
the work done by Q = Q Days
the work done by R = R days
According to Question :-
1) P and Q can do a piece of work in 12days
One work done by both P and Q together = 1/12 day
P + Q = 1/12
2) Q and R can do a piece of work in 18 days.
One work done by both R and Q together = 1/18 day
R + Q = 1/18
3) R and P can do a piece of work in 15days.
One work done by both R and P together = 1/15 day
P + R = 1/15
Adding all the equations what we have got :-
P + Q + R + Q + P + R = 1/12 + 1/18 + 1/15
Since , L.C.M of 12 , 18 , 15 = 180
R =
R = 7/360
Therefore work done by R in one day = 7/360
Total work done by 'R' alone = 1/7/360 = 360/7
≈ 51.4 days