Q1. Three pipes P, Q and R can fill a tank in 6 hours. After working at it together for 2 hours, R is closed and both P and Q can fill the remaining part in 7 hours. The number of hours that will be taken by R alone to fill the tank is
A 10
B 12
C 14
D 16
EXPLANATION
C
It is given that P, Q and R together can complete the work in 6 hrs.
P, Q and R together worked for 2 hours, this implies they completed 1/3rd of the work.
R left and remaining work is finished by P and Q in 7 hours.
Therefore, P and Q completed 2/3rd of the work in 7 hours.
This implies P and Q together can complete the work in 21/2 hours.
Let the total work be LCM(6, 21/2), i.e. 42 units.
P, Q and R together can complete 7 units in one hour.
P and Q together can complete 4 units in one hour.
This implies, R can complete 3 units in one hour.
Time taken by R alone to complete the work = 42 / 3 = 14 hours
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