P and Q can do a piece of work in 36days, Q and R can do it in 60days, and P and R can do it in 45days. When P, Q and R work together, how much work is finished by them in 5days?
- A10
1
- B8
1
- C5
1
- D6
1
Solution & Step-by-step Explanation
Let the total work be the LCM of 36, 60, and 45:
Total Work=LCM(36,60,45)=180units
Now, find the combined efficiencies:
Efficiency of (P+Q)=
36
180
=5units/day
Efficiency of (Q+R)=
60
180
=3units/day
Efficiency of (P+R)=
45
180
=4units/day
Adding all three equations:
2(P+Q+R)=5+3+4=12units/day
Efficiency of (P+Q+R)=
2
12
=6units/day
Work done by P, Q, and R together in 5days:
Work done=6×5=30units
The fraction of work finished is:
Fraction=
Total Work
Work Done
=
180
30
=
6
1
Total Work=LCM(36,60,45)=180units
Now, find the combined efficiencies:
Efficiency of (P+Q)=
36
180
=5units/day
Efficiency of (Q+R)=
60
180
=3units/day
Efficiency of (P+R)=
45
180
=4units/day
Adding all three equations:
2(P+Q+R)=5+3+4=12units/day
Efficiency of (P+Q+R)=
2
12
=6units/day
Work done by P, Q, and R together in 5days:
Work done=6×5=30units
The fraction of work finished is:
Fraction=
Total Work
Work Done
=
180
30
=
6
1