1️⃣ If a pipe can fill a tank in 4 hours, what fraction of the tank is filled in 1 hour?
Step-by-Step Explanation
The pipe fills the entire tank in 4 hours.
Therefore, in 1 hour, it fills 1/4 of the tank.
Answer: 1/4 ✅
2️⃣ If a pipe can empty a tank in 3 hours, what fraction of the tank is emptied in 1 hour?
Step-by-Step Explanation
The pipe empties the entire tank in 3 hours.
Therefore, in 1 hour, it empties 1/3 of the tank.
Answer: 1/3 ✅
3️⃣ If a pipe fills 1/5 of a tank in 1 hour, how long will it take to fill the entire tank?
Step-by-Step Explanation
If 1/5 of the tank is filled in 1 hour.
Then the whole tank will be filled in 5 hours.
Answer: 5 hours ✅
4️⃣ If a pipe can fill a tank in 6 hours, what part of the tank will it fill in 3 hours?
Step-by-Step Explanation
The pipe fills the whole tank in 6 hours.
Therefore, in 1 hour, it fills 1/6 of the tank.
In 3 hours, it will fill 3 * (1/6) of the tank.
3/6 simplifies to 1/2.
Answer: 1/2 ✅
5️⃣ If a pipe can empty 1/4 of a tank in 1 hour, how long will it take to empty the entire tank?
Step-by-Step Explanation
If 1/4 of the tank is emptied in 1 hour.
Then the whole tank will be emptied in 4 hours.
Answer: 4 hours ✅
6️⃣ A pipe can fill a tank in 8 hours, and another pipe can empty it in 12 hours. If both pipes are opened, how long will it take to fill the tank?
Step-by-Step Explanation
The filling rate of the first pipe is 1/8 per hour.
The emptying rate of the second pipe is 1/12 per hour.
The net filling rate is (1/8) - (1/12).
To subtract the fractions, find a common denominator, which is 24.
(3/24) - (2/24) = 1/24.
Therefore, it will take 24 hours to fill the tank.
Answer: 24 hours ✅
7️⃣ Pipe A can fill a tank in 10 hours, and pipe B can fill it in 20 hours. If both pipes are opened simultaneously, how much time will they take to fill the tank?
Step-by-Step Explanation
Pipe A's filling rate is 1/10 per hour.
Pipe B's filling rate is 1/20 per hour.
The combined filling rate is (1/10) + (1/20).
Find a common denominator, which is 20.
(2/20) + (1/20) = 3/20.
The time taken to fill the tank is 20/3 hours.
20/3 is equal to 6 2/3 hours.
Answer: 6 2/3 hours ✅
8️⃣ A cistern has two pipes. One can fill it in 6 hours, and the other can empty it in 3 hours. If both pipes are opened when the cistern is 1/2 full, how long will it take to empty the cistern?
Step-by-Step Explanation
The filling rate is 1/6 per hour.
The emptying rate is 1/3 per hour.
The net emptying rate is (1/3) - (1/6).
Find a common denominator, which is 6.
(2/6) - (1/6) = 1/6.
The cistern is 1/2 full.
The time to empty it is (1/2) / (1/6).
(1/2) * (6/1) = 3 hours.
Answer: 3 hours ✅
9️⃣ Two pipes A and B can fill a tank in 12 minutes and 15 minutes respectively. If both the pipes are opened simultaneously, after how much time should pipe B be closed so that the tank is full in 8 minutes?
Step-by-Step Explanation
Pipe A's filling rate is 1/12 per minute.
Pipe B's filling rate is 1/15 per minute.
Let pipe B be closed after 'x' minutes.
Pipe A fills for 8 minutes, and pipe B fills for 'x' minutes.
The equation is (8/12) + (x/15) = 1.
Simplify 8/12 to 2/3.
(2/3) + (x/15) = 1.
x/15 = 1 - (2/3).
x/15 = 1/3.
x = 15/3.
x = 5 minutes.
Answer: 5 minutes ✅
🔟 Three pipes A, B, and C can fill a tank in 4 hours. After working at it together for 1 hour, C is closed, and A and B can fill the remaining part in 5 hours. The number of hours taken by C alone to fill the tank is?