1. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both taps are opened simultaneously, then after how much time will the cistern get filled ?

**Answer: **7.2 hours

**Explanation:**
Time taken by tap A to fill the cistern=4 hrs

so work done by tap A in 1 hour = 1/4th

Time taken by tap B to empty the full cistern = 9 hours

so work done by tap B in 1 hour = 1/9th

=> Work done by (A + B) in 1 hour=(1/4 - 1/9)=5/36

Therefore, the tank will fill the cistern = 36/5 hours=7.2 hours.

2. A pump can fill a tank with water in 2 hours. Because of a leak, it took hours to fill the tank. The leak can drain all the water of the tank in:

**Answer: **14 hours

**Explanation:**
Work Done by the leak in 1 hrs = (1/2-3/7) = 1/14

so leak will empty the tank in 14 hrs.

3. Pipe A can fill a tank in 8 hours and Pipe B can fill it in 6 hours. If both the pipes are opened but after 2 hours pipe A is closed, then the other pipe will fill the tank in

**Answer: **2 1/2 hours

**Explanation:**
Tank part filled by Pipe A in 1 hour = 1/8

or

Time taken to fill 1/8 part of tank filled A = 1 hour ------------- (1)

Tank part filled by Pipe B in 1 hours = 1/6

or

Time taken to fill 1/6 part of tank filled B = 1 hour ---------(2)

=> Tank Part filled by (A+B) in 1 hour = (1/8 + 1/6)

=> Tank Part filled by (A+B) in 2 hour = 2*(1/8 + 1/6) = 2*(3+4)/24 = 2*7/24 = 7/12

After 2 hours left over portion of tank = (1-7/12) = 5/12

Time taken to fill 1/6 part of tank filled B = 1 hour

so time taken to fill 5/12 part of tank by B = 6 * 5/12 = 5/2 = 2 1/2

=> So it takes 2 1/2 hrs (2hrs 30 min) to fill 5/12 of tank.

4. Two pipes A and B can fill a tank in 9 hours and 3 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours will the tank be full?

**Answer: **5 hrs

**Explanation:**
Tank part filled by pipe A in 1 hour =1/9

Tank part filled by pipe B in 1 hour =1/3

Given Pipe A and B are opened alternatively.

So Part filled in every 2 hours =(1/9+1/3)=4/9

Tank Part will be filled in 4 hour =2*4/9=8/9

Remaining part = (1-8/9)=1/9

So next is A turn.

So Pipe A will fill remaining 1/9 part in next 1 hour.

Total Time = (4 hrs + 1 hrs) = 5 hrs.

5. A pump takes 8 hours to fill an overhead tank, but due to an open tap in the kitchen, the time taken is 10 hours. In how much time would the kitchen tap empty a full overhead tank?

**Answer: **40 hours

**Explanation:**
Here is no explanation for this answer

6. Pipe A can fill a cistern in 6 hours less than Pipe B. Both the pipes together can fill the cistern in 4 hours. How much time would A take to fill the cistern all by itself?

**Answer: **6 hours

**Explanation:**
Let's assume time required by Pipe A to fill the cistern = X hours

So Time required by Pipe B to fill the cistern = (X + 6) hours

? Both Pipes (A+B) can fill cistern in 1 hour = [1/X + 1/(X + 6)]

Given Both pipe fill the cistern in 4 hours

=> [1/X + 1/(X + 6)] = 1/4 => [(X+6) + X]/(X+6)*x = 1/4

4X + 24 + 4X = X2 + 6x

X2 - 2X - 24 = 0

(X-6)(X+4) = 0

=> A can fill cistern in 6 hours.

7. 12 buckets of water fill a tank when the capacity of each tank is 13.5 liters. How many buckets will be needed to fill the same tank,if the capacity of each bucket is 9 liters?

**Answer: **18

**Explanation:**
Capacity of the tank =(12 x 13.5) liters =162 liters.

Capacity of each bucket =9 liters

Number of buckets needed = 162/9 =18.

8. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 min, then the slower alone will be able to fill the tank in:

**Answer: **144 min

**Explanation:**
Lets assume time required by slower pipe alone to fill the tank = x minutes.

Then, faster pipe will fill it in x/3 minutes.

=> 1/x+3/x = 1/36

=>4/x = 1/36 => x = 144 min.

9. A tap supplies 8 litres of water per minute into a cistern. A leak at the bottom of the cistern can empty the cistern in 10 hours. A full tank with the tap open is emptied by the leak in 15 hours. What is the capacity of the tank?

**Answer: **14400 litres

**Explanation:**
Tank can be emptied by leak in 1 hour = 1/10

or

Time required to emptied 1/10 part of tank = 1 hour

Given full tank can be emptied by leak = 15 hours

or time need to emptied 1/15 part of tank by leak = 1 hours

so (1/10 - 1/15) part can be filled by tap = 1 hours

=> 1/30 part can be filled by tap = 1 hours

or

Time needed to fill the cistern by tap = 30 hours = 1800 minutes

so Capacity of cistern = 8 * 1800 = 14400 liters

10. Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?

**Answer: **17 1/7 min

**Explanation:**
Cistern part filled by pipe A in 1 min = 1/20

and by pipe B in 1 min = 1/30

Pipe C empty cistern in 1 min = 1/40 part.

When all pipes are open Cistern part will be filed = (1/20+1/30-1/40) = 7/120

=> Time required to fill the cistern = 120/7 = 17 1/7 min.