Quantitative Aptitude Quiz – 82

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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
e) None of these

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Answer c) 30 h
Explanation:
Short-cut method,
Here, m = 20 and n = 12
Then, T = (m*n)/(m-n) = (12*20)/8 = 30 h.

2. A tank has a leak which would empty it in 8 h. A tap is turned on which admits 3 L a min into the tank and it is now emptied in 12 h. How many litres does the tank hold?
a) 4320 L
b) 4000 L
c) 2250 L
d) 4120 L
e) None of these

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Answer a) 4320 L
Explanation:
Work done by the inlet in 1 h = (1/8 – 1/12) = 1/24
Work done by the inlet in 1 min = 1/24 * 1/60 = 1/1440
Volume of 1/1440 part = 3 L
Then, Volume of the whole = 3 * 1440 = 4320 L.

3. A tap having diameter ‘d’ can empty a tank in 40 min. How long another tap having diameter ‘2d’ take to empty the same tank?
a) 5 min
b) 20 min
c) 10 min
d) 40 min
e) None of these

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Answer c) 10 min
Explanation:
Area of tap (directly proportional) Work done by pipe.
When diameter is doubled, area will be four times. SO, it will work four times faster.
Hence, required time taken to empty the tank = 40 * 1/4 = 10 min.

4. Two pipes A and B can fill a tank in 24 and 32 min, respectively. If both the pipes are opened together, after how much time pipe B should be closed so that the tank is full in 9 min?
a) 40 min
b) 30 min
c) 10 min
d) 20 min
e) None of these

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Answer d) 20 min
Explanation:
By using direct formula,
Here, X = 24 min, Y = 32 min, T = 9 min
Required time = Y(1 – T/X) = 32(1 – 9/24) = 32 * 15/24 = 20 min.

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) 45 min
b) 38 min
c) 22 min
d) 42 min
e) None of these

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Answer a) 45 min
Explanation:
Let the number of min taken to empty the cistern be X min.
According to the question,
X/6 – (X+5)/12 – (X+5)/15 = 0
=>X/6 – X/12 – 5/12 – X/15 – 5/15 = 0
=>X/6 – X/12 – X/15 = 5/12 + 5/15
=>(10X – 5X – 4X)/60 = (25+20)/60
=>X/60 = 45/60 =>X = 45 min.

6. Capacity of tap B is 80% more than that of A. If both the taps are opened simultaneously, they take 45 h to fill the tank. How long will B take to fill the tank alone?
a) 72 h
b) 70 h
c) 48 h
d) 66 h
e) None of these

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Answer b) 70 h
Explanation:
Let time taken by B to fill the tank,
a = X h.
Time taken by A to fill the tank,
b = X + (X*80)/100 = 9X/5 h
According to the formula,
Time taken by both the taps to fill the tank = T = ab/(a+b)
=>45 = (X * 9X/5) / (X + 9X/5)
By Solving this, X = 70h.

7. Two taps A and B can fill a tank in 25 min and 20 min, respectively. But taps are not opened properly, so the taps A and B allow 5/6 th and 2/3 rd part of water, respectively. How long will they take to fill the tank?
a) 12 min
b) 13 min
c) 14 min
d) 15 min
e) None of these

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Answer d) 15 min
Explanation:
part of the tank filled with A and B in 1 min = 1/25 * 5/6 + 1/20 * 2/3 = 1/30 + 1/30 = 1/15
Hence, time taken to fill the tank = 15 min.

8. Three taps A, B and C fill a tank in 20 min, 15 min and 12 min, respectively. If all the taps are opened simultaneously, how long will they take to fill 40% of the tank?
a) 1 min
b) 2 min
c) 3 min
d) 4 min
e) None of these

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Answer b) 2 min
Explanation:
part of the tank filled in 1 min by A, B and C = 1/20 + 1/15 + 1/12 = 1/5
Time taken by A, B and C to fill = 5 min
Then, time taken by A, B and C to fill 40% of the tank = 40% of 5 = 2 min.

9. Two pipes A and B are opened together to fill a tank. Both pipes fill the tank in a certain time. If A separately takes 16 min more than the time taken by (A+B) and B takes 9 min more than the time taken by (A+B). Find the time taken by A and B to fill the tank when both the pipes are opened together?
a) 10 min
b) 12 min
c) 15 min
d) 8 min
e) None of these

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Answer b) 12 min
Explanation:
By short-cut
Here, a = 16 and b = 9
Required time = root(ab) = root(16 * 9) = 4 * 3 = 12 min.

10. Inlet A is four times faster than inlet B to fill a tank. If A alone can fill it in 15 min, how long will it take if both the pipes are opened together?
a) 10 min
b) 12 min
c) 15 min
d) 14 min
e) None of these

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Answer b) 12 min
Explanation:
Time taken by A to fill the tank, m = 15 min
Time taken by B to fill the tank,
n = 15 * 4 = 60 min
Required time taken = m*n/m+n = 15*60/(15+60) = 12 min.

Best Wishes,
D2G’s Team..