1). A tap can fill an empty tank in 12 h and a leakage can empty the tank in 20 h. If tap and leakage both work together, then how long will it take to fill the tank?
A). 25 h 
B). 40 h 
C). 30 h 
D). 35 h 
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2). Three taps A, B and C together can fill an empty cistern in 10 min. The tap A alone can fill it in 30 min and the tap B alone can fill it in 40 min. How long will the tap C alone take to fill it?
A). 16 min 
B). 24 min 
C). 32 min 
D). 40 min 
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3). Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?
A). \( \Large 8\frac{1}{4} \) 
B). \( \Large 8\frac{3}{4} \) 
C). 5 min 
D). \( \Large 8\frac{1}{2} \) 
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4). There are three pipes connected with a tank. The first pipe can fill \( \Large \frac{1}{2} \) part of the tank in 1 h, second pipe can fill \( \Large \frac{1}{3} \) part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, \( \Large 7\frac{1}{2} \) part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank?
A). 3 h 
B). 4 h 
C). 5 h 
D). 6 h 
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5). A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min, but a third pipe can empty it in 6 min. The first two pipes are kept open for 5 min in the beginning and then the third pipe is also opened. Time taken to empty the cistern is
A). 38 min 
B). 22 min 
C). 42 min 
D). 45 min 
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6). A cistern has three pipes A, B and C. Pipes A and B can fill it in 3 and 4 h, respectively, while pipe C can empty the completely filled cistern in 1 h. If the pipes are opened in order at 3:00 pm, 4:00 pm and 5:00 pm, respectively, at what time will the cistern be empty?
A). 6:15 pm 
B). 7:12 pm 
C). 8:12 pm 
D). 8:35 pm 
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7). Three pipes A, B and C can fill a tank in 30 min, 20 min and 10 min, respectively. When the tank is empty, all the three pipes are opened. If A, B and C discharge chemical solutions P, Q and R respectively, then the part of solution R in the liquid in the tank after 3 min is
A). \( \Large \frac{8}{11} \) 
B). \( \Large \frac{5}{11} \) 
C). \( \Large \frac{6}{11} \) 
D). \( \Large \frac{7}{11} \) 
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8). 2x + 3y = 29 and y = x + 3, what is the value of x?
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9). Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number of animal feet is 248, what is the total number of goats Deepak has?
A). 32 
B). 36 
C). 34 
D). Cannot be determined 
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10). The sum of the two digits is 15 and the difference between them is 3. What is the product of the digits?
A). 56 
B). 63 
C). 42 
D). 54 
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