1. A tank with capacity T liters is empty. If water flows into the tank from pipe X at the rate of x liters per minute and water is pumped out by Y at the rate of y liters per minute and x > y, then how many minutes will the tank be filled?

a) (x - y) 60 T minutes

b) (T - x) minutes

c) $$\frac{{\text{T}}}{{{\text{x}} - {\text{y}}}}$$ minutes

d) $$\frac{{\text{T}}}{{{\text{y}} - {\text{x}}}}$$ minutes

Explanation: Net volume filled in 1 minute

= (x - y) liters

The tank will be filled in

= $$\frac{{\text{T}}}{{\left( {x - y} \right)}}$$ minutes

2. A pipe can fill a tank in 3 hours. There are two outlet pipes from the tank which can empty it in 7 and 10 hours respectively. If all the three pipes are opened simultaneously, then the tank will be filled in -

a) 8 hours

b) 9 hourss

c) 10 hours

d) 11 hours

Explanation: Net part filled in 1 hour

$$\eqalign{ & {\text{ = }}\frac{1}{3} - \left( {\frac{1}{7} + \frac{1}{{10}}} \right) \cr & = \frac{1}{3} - \frac{{17}}{{70}} \cr & = \frac{{19}}{{210}} \cr} $$

The tank will be filled in $$\frac{{210}}{{19}}$$ hours i.e.

$$\eqalign{ & {\text{= 11}}\frac{1}{{19}}{\text{ hours}} \cr & \cong 11\,{\text{hours }} \cr} $$

3. A vessel has three pipes connected to it , two to supply liquid and one to draw liquid. The first alone can fill the vessel in $$4\frac{1}{2}$$ hours, the second in 3 hours and the third can empty it in $$1\frac{1}{2}$$ hours. If all the pipes are opened simultaneously when the vessel is half full, how soon will it be emptied?

a) $$4\frac{1}{2}$$ hours

b) $$5\frac{1}{2}$$ hours

c) $$6\frac{1}{2}$$ hours

d) None of these

Explanation:

$$\eqalign{ & {\text{Net part filled in 1 hour}} \cr & = \frac{2}{3} - \left( {\frac{2}{9} + \frac{1}{3}} \right) \cr & = \left( {\frac{2}{3} - \frac{5}{9}} \right) \cr & = \frac{1}{9} \cr & \therefore \,\frac{1}{9}\,:\,\frac{1}{2}\,::\,1\,:\,x \cr & {\text{or}}\,\,\,x = \left( {\frac{1}{2} \times 9} \right) = 4\frac{1}{2}{\text{ hours}} \cr & {\text{So, the tank will be emptied in}} \cr & {\text{ = }}4\frac{1}{2}{\text{ hours}} \cr} $$

4. Two pipe A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C are open together to fill the tank in 15 minutes, find the capacity of tank?

a) 180 gallons

b) 150 gallons

c) 120 gallons

d) 60 gallons

Explanation: Work done by the C pipe in 1 minute

$$\eqalign{ & = \frac{1}{{15}} - \left( {\frac{1}{{20}} + \frac{1}{{24}}} \right) \cr & = \left( {\frac{1}{{15}} - \frac{{11}}{{120}}} \right) \cr & = - \frac{1}{{40}}\,\left[ { - {\text{ve}}\,{\text{means}}\,{\text{emptying}}} \right] \cr} $$

Volume of $$\frac{1}{{40}}$$ part = 3 gallons.

Volume of whole = (3 × 40) gallons = 120 gallons

5. Three pipes P, Q and R can separately fill a cistern in 4, 8 and 12 hours respectively. Another pipe S can empty the completely filled cistern in 10 hours. Which of the following arrangements will fill the empty cistern in less time than others?

a) Q alone is open

b) P, R and S are open

c) P and S are open

d) P, Q and S are open

Explanation:

$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(Total Capacity)}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{120}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\overline { \downarrow \,\,\,\,\,\,\,\,\,\, \downarrow \,\,\,\,\,\,\,\,\,\,\, \downarrow \,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow } \cr & {\text{efficiency 30}}\,\,\,\,\,\,15\,\,\,\,\,\,\,\,10\,\,\, - 12 \cr & {\text{hours}} \to \,\,\mathop 4\limits_{\left( {\text{P}} \right)}^ \downarrow \,\,\,\,\,\,\mathop 8\limits_{\left( {\text{Q}} \right)}^ \downarrow \,\,\,\,\,\,\,\mathop {12}\limits_{\left( {\text{R}} \right)}^ \downarrow \,\,\,\,\,\,\,\,\,\,\,\mathop {10}\limits_{\left( {\text{S}} \right)}^ \downarrow \cr} $$

In order to fill the cistern in less time.

So, efficiency of filling should be more

now, check all options

(A) → Q efficiency 15 units/hr

(B) → (P + R - S) efficiency

= 30 + 10 - 12 = 28 units/hr

(C) → (P - S) efficiency

= 30 - 12 = 18 units/hr

(D) → (P + Q - S) efficiency

= 30 + 15 - 12 = 33 units/hr

Since efficiency of option (D) is highest.

6. Two pipes A and B can fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is one - third full, a leak develops in the tank through which one - third water supplied by both the pipes gose out. The total time taken to fill the tank is?

a) 12 hours

b) 14 hours

c) 16 hours

d) 18 hours

Explanation: Part filled by (A + B) in 1 hour

$$\eqalign{ & {\text{= }}\left( {\frac{1}{{20}} + \frac{1}{{30}}} \right) \cr & = \frac{1}{{12}} \cr} $$

So, A and B together can fill the tank in 12 hrs,

$$\frac{1}{3}$$ part is filled by (A + B) in

$$\left( {\frac{1}{3} \times 12} \right){\text{ = 4 hrs}}$$

Since the leak empties one - third water, so time taken to fill the tank

= Time taken by (A + B) to fill the whole tank + Time taken by (A + B) to fill one - third tank

= (12 + 4)

= 16 hours

7. Two pipes can fill a tank in 40 and 48 minutes respectively and a waste pipe can empty 3 gallons per minutes. All the three pipes working together can fill the tank in 30 minutes, The capacity of the tank is-

a) 60 gallons

b) 120 gallons

c) 180 gallons

d) 240 gallons

Explanation: Work done by the waste pipe in 1 minute

$$\eqalign{ & {\text{ = }}\frac{1}{{30}} - \left( {\frac{1}{{40}} + \frac{1}{{48}}} \right) \cr & = \left( {\frac{1}{{30}} - \frac{{11}}{{220}}} \right) \cr & = - \frac{1}{{80}}\left[ { - \,{\text{Nagetive sign means emptying}}} \right] \cr & {\text{Volume of }}\frac{1}{{80}}{\text{ part = 3 galons}} \cr & {\text{Volume of whole tank}} \cr & {\text{ = }}\left( {3 \times 80} \right){\text{gallons}} \cr & {\text{ = 240 gallons}}{\text{}} \cr} $$

8. An outlet pipe can empty a cistern in 3 hours. In what time will empty $$\frac{2}{3}$$ of the cistern?

a) 3 hours

b) 5 hours

c) 2 hours

d) 4 hours

Explanation: The outlet pipe empties the one complete cistern in 3 hours

Time taken to empty $$\frac{2}{3}$$ Part of the cistern

$$\eqalign{ & {\text{= }}\frac{2}{3} \times 3 \cr & = 2\,{\text{hours}} \cr} $$

9. A tank is 7 metre long and 4 meter wide wide. At what speed should water run through a pipe 5 cm broad and 4 cm deep so that in 6 hours and 18 minutes water level in the tank rises by 4.5 meter ?

a) 10 km/hours

b) 12 km/hours

c) 8 km/hours

d) None of these

Explanation: Rate of flow of water = x cm/minute

Volume of water that flowed in the in 1 minutes

= (5 × 4 × x) = 20 x cu.cm.

Volume of water that flowed in the tank in 6 hours 18 minutes.

i.e. (6 × 60 + 18) = 378 minutes

= 2x × 378 cu. cm.

According to question,

$$\eqalign{ & {\text{20}}x \times 378 = 700 \times 400 \times 450 \cr & x = \left( {\frac{{700 \times 400 \times 450}}{{20 \times 378}}} \right){\text{cm /minutes}} \cr & x = \left( {\frac{{700 \times 400 \times 450 \times 60}}{{100000 \times 20 \times 378}}} \right){\text{km/hours}} \cr & x{\text{ = 10 km/hours}} \cr} $$

10. Two pipes can fill a tank in 12 hours and 16 hours respectively. A third pipe can empty the tank in 30 hours. If all three pipes are opened and functions simultaneously, how much time will the tank take to be full?( in hours )

a) $$10\frac{4}{9}$$

b) $$9\frac{1}{2}$$

c) $$8\frac{8}{9}$$

d) $$7\frac{2}{9}$$

Explanation: First pipe fill the tank in 1 hour = $$\frac{1}{{12}}$$ part of tank

Second pipe fill the tank in 1 hour = $$\frac{1}{{16}}$$ part of tank

Third pipe empty the tank in 1 hour = $$\frac{1}{{30}}$$ part of tank

When all three pipes are opened simultaneously, part of the tank filled in 1 hour

$$ = \frac{1}{{12}} + \frac{1}{{16}} - \frac{1}{{30}}$$

LCM of 12, 16 and 30 = 240

$$\eqalign{ & {\text{ = }}\frac{{20 + 15 - 8}}{{240}} \cr & = \frac{{27}}{{240}} \cr} $$

Required time taken by all the three pipes

$${\text{ = }}\frac{{240}}{{27}} = \frac{{80}}{9} = 8\frac{8}{9}\,{\text{Hours}}$$