P, Q and R together can do a piece of work in 56 days. P and Q together can do one-fourth as much work as R alone. In how many days can P and Q together complete the entire work?
- A140
- B70
- C280
- D210
Solution & Step-by-step Explanation
Let the efficiencies of P, Q, and R be P, Q, and R respectively.
From the problem statement:
P+Q=
4
1
R⟹4(P+Q)=R
The combined efficiency of all three working together is:
Total Efficiency=(P+Q)+R
Substitute R=4(P+Q) into the total efficiency:
Total Efficiency=(P+Q)+4(P+Q)=5(P+Q)
We know that P, Q, and R together complete the work in 56 days:
Total Work=Total Efficiency×Time=5(P+Q)×56=280(P+Q)
Now, we need to find the number of days required by P and Q together to finish the entire work:
Days=
Efficiency of (P + Q)
Total Work
=
(P+Q)
280(P+Q)
=280days
From the problem statement:
P+Q=
4
1
R⟹4(P+Q)=R
The combined efficiency of all three working together is:
Total Efficiency=(P+Q)+R
Substitute R=4(P+Q) into the total efficiency:
Total Efficiency=(P+Q)+4(P+Q)=5(P+Q)
We know that P, Q, and R together complete the work in 56 days:
Total Work=Total Efficiency×Time=5(P+Q)×56=280(P+Q)
Now, we need to find the number of days required by P and Q together to finish the entire work:
Days=
Efficiency of (P + Q)
Total Work
=
(P+Q)
280(P+Q)
=280days