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21. 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. $\frac{T}{x - y}$ minutes

D. $\frac{T}{y - x}$ minutes

Discuss

Solution:

Net volume filled in 1 minute
= (x - y) liters
∴ The tank will be filled in
=

\frac{T}{(x - y)}

minutes

22. 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 hours

C. 10 hours

D. 11 hours

Discuss

Solution:

Net part filled in 1 hour

\begin{aligned} = \frac{1}{3} - (\frac{1}{7} + \frac{1}{10}) \\ = \frac{1}{3} - \frac{17}{70} \\ = \frac{19}{210} \end{aligned}

∴ The tank will be filled in

\frac{210}{19}

hours i.e.

\begin{aligned} =  11 \frac{1}{19} hours \\ ≅ 11 hours \end{aligned}

23. 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

Discuss

Solution:

\begin{aligned} Net part filled in 1 hour \\ = \frac{2}{3} - (\frac{2}{9} + \frac{1}{3}) \\ = (\frac{2}{3} - \frac{5}{9}) \\ = \frac{1}{9} \\ ∴ \frac{1}{9} : \frac{1}{2} :: 1 : x \\ or x = (\frac{1}{2} \times 9) = 4 \frac{1}{2} hours \\ So, the tank will be emptied in \\ = 4 \frac{1}{2} hours \end{aligned}

24. 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

Discuss

Solution:

Work done by the C pipe in 1 minute

\begin{aligned} = \frac{1}{15} - (\frac{1}{20} + \frac{1}{24}) \\ = (\frac{1}{15} - \frac{11}{120}) \\ = - \frac{1}{40} [- ve means emptying] \end{aligned}

∴ Volume of

\frac{1}{40}

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

25. 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

Discuss

Solution:

\begin{aligned} (Total Capacity) \\ 120 \\ \bar{↓ ↓ ↓ ↓} \\ efficiency 30 15 10 - 12 \\ hours \to 4_{(P)}^{↓} 8_{(Q)}^{↓} 12_{(R)}^{↓} 10_{(S)}^{↓} \end{aligned}

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
Option (D) is answer
Since efficiency of option (D) is highest

26. A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank , the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?

A. 2400 litters

B. 4500 litters

C. 1200 litters

D. 7200 litters

Discuss

Solution:

Let the total capacity of the tank is 30 units.
The efficiency of Leakage(Pipe A) will be

\frac{30}{10}

= 3
And the efficiency of the leakage (Pipe A) and another Pipe (B) which is filling the tank will be

\frac{30}{15}

= 2
Pipe A is emptying at 3 units/hr and when filling pipe B started then the emptying rate will come down to 2 units/hr.
∴ Filling Pipe B efficiency is 3 - 2 = 1unit/hr
Pipe B will be fill the tank in

\frac{30}{1}

= 30 hrs
Filling rate of Pipe B per minute is 4 litter
∴ Total Capacity of tank will be = (4 × 60) × 30 = 7200 litters

27. A pump can fill a tank with water in 2 hours. Because of a leak, it took $2 \frac{1}{3}$ hours to to fill the tank. The leak can drain all the water of the tank in?

A. $4 \frac{1}{3}$ hours

B. 7 hours

C. 8 hours

D. 14 hours

Discuss

Solution:

Work done by the leak in 1 hour

\begin{aligned} = (\frac{1}{2} - \frac{3}{7}) = \frac{1}{14} \end{aligned}

∴ Leak will empty the tank in 14 hours

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

A. 81 min

B. 108 min

C. 144 min

D. 192 min

Discuss

Solution:

Let the slower pipe alone fill the tank in x minutes
Then, Faster pipe alone will fill it in

\frac{x}{3}

minutes

\begin{aligned} ∴ \frac{1}{x} + \frac{3}{x} = \frac{1}{36} \\ \Rightarrow \frac{4}{x} = \frac{1}{36} \\ \Rightarrow x = 144 \end{aligned}

So slower pipe alone will fill the tank in 144 min.

29. A swimming pool is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?

A. 6 hours

B. 10 hours

C. 15 hours

D. 30 hours

Discuss

Solution:

Suppose first pipe alone takes x hours to fill the tank.
Then second and third pipes will takes (x - 5) and (x - 9) hours respectively to fill the tank.

\begin{aligned} ∴ \frac{1}{x} + \frac{1}{(x - 5)} = \frac{1}{(x - 9)} \\ \Rightarrow \frac{x - 5 + x}{x (x - 5)} = \frac{1}{(x - 9)} \\ \Rightarrow (2 x - 5) (x - 9) = x (x - 5) \\ \Rightarrow x^{2} - 18 x + 45 = 0 \\ \Rightarrow (x - 15) (x - 3) = 0 \\ \Rightarrow x = 15 [neglecting x =  3] \end{aligned}

So, first pipe alone takes 15 hrs to fill the tank.

30. 12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?

A. 8

B. 15

C. 16

D. 18

Discuss

Solution:

Capacity of the tank
= (12 × 13.5) litres
= 162 litres
Capacity of each bucket = 9 litres
Number of buckets needed

\begin{aligned} = (\frac{162}{9}) \\ = 18 \end{aligned}

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