Practice Questions
Pipe A fills a tank in 8 hours and Pipe B fills it in 12 hours. Both are opened together, but after 2 hours B is closed. Find total time to fill the tank.
One hour 함께 = $1/8+1/12 = 5/24$. In 2 hours, $10/24 = 5/12$ filled. Remaining = $7/12$. Time for A = $(7/12)/(1/8) = 56/12 = 4.67$ hours. Total = $2 + 4.67 = 6.67$ hours.
A pipe can fill a tank in 10 hours and a leak can empty it in 15 hours. If both operate together, how long will the tank take to fill?
Net rate = $1/10 - 1/15 = 1/30$. Time = 30 hours.
Three pipes can fill a tank in 6, 8 and 12 hours respectively. If all are opened together, how long will it take to fill the tank?
Net rate = $1/6 + 1/8 + 1/12 = (4+3+2)/24 = 9/24 = 3/8$. Time = $8/3 = 2.67$ hours.
A cistern is filled by two pipes in 20 minutes. If one pipe alone can fill it in 30 minutes, find the time taken by the second pipe alone.
$1/20 - 1/30 = 1/60$. Time = 60 minutes.
A tank is filled in 5 hours. After 3 hours, a leak develops which empties the full tank in 10 hours. Find the total time to fill the tank.
In 3 hours, $3/5$ filled. Remaining $2/5$ filled at rate $(1/5-1/10)=1/10$. Time for remaining = $(2/5)/(1/10) = 4$ hours. Total = $3+4=7$ hours.
Two pipes fill a tank in 12 and 15 hours respectively, and a third pipe empties it in 20 hours. If all are opened together, find the net time required.
Net rate = $1/12 + 1/15 - 1/20 = (5+4-3)/60 = 6/60 = 1/10$. Time = 10 hours.
A tap fills a tank in 8 hours. After half the tank is filled, three more similar taps are opened. Find total time to fill the tank.
First half: 4 hrs (one tap). Remaining half: 4 taps fill at rate $4 \times 1/8 = 1/2$ per hr. Time = $(1/2)/(1/2) = 1$ hr. Total = $4+1 = 5$ hrs.
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. A third pipe C can empty it in 40 minutes. If all three are opened together, how long will it take to fill the tank?
Net rate = $1/20 + 1/30 - 1/40 = (6+4-3)/120 = 7/120$. Time = $120/7 \approx 17.14$ min.
Pipe A fills a tank in 6 hours and Pipe B fills it in 8 hours. Pipe C empties it in 12 hours. A and B are opened together for 2 hours, then C is also opened. Find total time.
A+B rate = $1/6+1/8 = 7/24$. In 2 hrs: $7/12$ filled. Remaining = $5/12$. Net rate with C = $7/24 - 1/12 = 5/24$. Time = $(5/12)/(5/24) = 2$ hrs. Total = $2+2 = 4$ hrs.
A cistern has two inlets that can fill it in 12 and 15 minutes respectively. An outlet can empty it in 10 minutes. If all three are opened together, will the cistern fill or empty? In what time?
Net rate = $1/12 + 1/15 - 1/10 = (5+4-6)/60 = 3/60 = 1/20$ (positive, so fills). Time = 20 minutes.
Premium Content
Unlock Pipes and Cisterns Quiz and all premium lessons with a subscription.
From ₹199.99/year — See plans