Question
The efficiency of pipe R is 60% more than the efficiency
of pipe S. Pipe Q alone can fill 30% of the empty tank in 6 hours. Pipe R alone can fill an empty tank completely in (y-5) hours. The ratio between the efficiencies of pipe P and R is 5:6 respectively. Pipe P and Q together can fill 25% of the empty tank in 3 hours. Find out the time taken by pipe S alone to fill 55% of the tank and the value of ‘y’.Solution
Let’s assume the capacity of the tank is 600 units.
Pipe Q alone can fill 30% of the empty tank in 6 hours.
Time taken by Pipe Q alone to fill the tank completely = (6/30)x100
= 20 hours
Efficiency of pipe Q = 600/20 = 30 units/hour Eq.(i)
Pipe P and Q together can fill 25% of the empty tank in 3 hours.
Time taken by Pipe P and Q together to fill the tank completely = (3/25)x100
= 12 hours
Efficiency of pipe P and Q together = 600/12 = 50 units/hour Eq.(ii)
Efficiency of pipe P = Eq.(ii)-Eq.(i)
= 50-30
= 20 units/hour
The ratio between the efficiencies of pipe P and R is 5:6 respectively.
Efficiency of pipe R = (20/5)x6
= 24 units/hour
The efficiency of pipe R is 60% more than the efficiency of pipe S.
24 = (100+60)% of the efficiency of pipe S
24 = 160% of the efficiency of pipe S
efficiency of pipe S = 24/1.6
= 240/16
= 15 units/hour
Pipe R alone can fill an empty tank completely in (y-5) hours.
(Efficiency of pipe R) x (time taken by pipe R to fill an empty tank completely) = total capacity of the tank
24 x (y-5) = 600
4 x (y-5) = 100
(y-5) = 25
y = 25+5
y = 30
Time taken by pipe S alone to fill 55% of the tank = 55% of (total capacity of the tank)/(efficiency of pipe S)
= 55% of (600)/(15)
= 55% of 40
= 22 hours
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