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Q:

P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?

A) 60/11	B) 61/11
C) 71/11	D) 72/11

Answer & Explanation Answer: A) 60/11

Explanation:

P can complete the work in (12 x 8) hrs = 96 hrs

Q can complete the work in (8 x 10) hrs=80 hrs

Therefore, P's 1 hour work=1/96 and Q's 1 hour work= 1/80

(P+Q)'s 1 hour's work =(1/96) + (1/80) = 11/480. So both P and Q will finish the work in 480/11 hrs

Therefore, Number of days of 8 hours each = (480/11) x (1/8) = 60/11

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Filed Under: Time and Work

Q:

A, B and C can complete a piece of work in 24,6 and 12 days respectively.Working together, they will complete the same work in:

A) 1/24 days	B) 7/24 days
C) 24/7 days	D) 4 days

Answer & Explanation Answer: C) 24/7 days

Explanation:

(A+B+C)'s 1 day's work = (1/24 + 1/6 + 1/12) = 7/24

so, A,B and C together will complete the work in 24/7 days.

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Filed Under: Time and Work

Q:

A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 $m^{3}$ . The emptying capacity of the tank is 10 $m^{3}$ per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

A) 50 m^3/min	B) 60 m^3/min
C) 72 m^3/min	D) None of these

Answer & Explanation Answer: A) 50 m^3/min

Explanation:

Let the filling capacity of the pump be x $m^{3}$ /min.

Then, emptying capacity of the pump=(x+10) $m^{3}$ /min.

so, $\frac{2400}{x} - \frac{2400}{x + 10} = 8 \Leftrightarrow x^{2} + 10 x - 3000 = 0$

$\Rightarrow (x - 50) + (x + 60) = 0 \Leftrightarrow x = 50$

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Filed Under: Pipes and Cistern
Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

Q:

Three taps A,B and C can fill a tank in 12,15 and 20 hours respectively. If A is open all the time and B ,C are open for one hour each alternatively, the tank will be full in:

A) 6 hrs	B) 20/3 hrs
C) 7 hrs	D) 15/2 hrs

Answer & Explanation Answer: C) 7 hrs

Explanation:

$(A + B)' s 1 h o u r w o r k = (\frac{1}{12} + \frac{1}{15}) = \frac{9}{60} = \frac{3}{20}$

$(A + C)' s 1 h o u r w o r k = (\frac{1}{12} + \frac{1}{20}) = \frac{8}{60} = \frac{2}{15}$

$p a r t f i l l e d i n 2 h r s = (\frac{3}{20} + \frac{2}{15}) = \frac{17}{60}$

$p a r t f i l l e d i n 6 h r s = (3 * \frac{17}{60}) = \frac{17}{20}$

$r e m a i n i n g p a r t = (1 - \frac{17}{20}) = \frac{3}{20}$

Now, it is the turn of A and B (3/20) part is filled by A and B in 1 hour.

Therefore, Total time taken to fill the tank =(6+1)hrs= 7 hrs

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Filed Under: Pipes and Cistern

Q:

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?

A) 8	B) 15
C) 16	D) 18

Answer & Explanation Answer: D) 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.

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Filed Under: Pipes and Cistern

Q:

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:

A) 81 min	B) 108 min
C) 144 min	D) 192 min

Answer & Explanation Answer: C) 144 min

Explanation:

Let the slower pipe alone fill the tank in x minutes.

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

$= > \frac{1}{x} + \frac{3}{x} = \frac{1}{36} = > \frac{4}{x} = \frac{1}{36} = > x = 144 m i n s$

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Filed Under: Pipes and Cistern

Q:

A water tank is two-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?

A) 6 min.to empty	B) 6 min.to fill
C) 9 min.to empty	D) 9 min.to fill

Answer & Explanation Answer: A) 6 min.to empty

Explanation:

Clearly,pipe B is faster than pipe A and so,the tank will be emptied.

part to be emptied = 2/5

part emptied by (A+B) in 1 minute= $(\frac{1}{6} - \frac{1}{10}) = \frac{1}{15}$

$\frac{1}{15} : \frac{2}{5} : : 1 : x$

$\frac{2}{5} * 15 = 6 m i n s$

so, the tank will be emptied in 6 min

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Filed Under: Pipes and Cistern

Q:

If $a = \frac{\sqrt{5} + 1}{\sqrt{5} - 1} b = \frac{\sqrt{5} - 1}{\sqrt{5} + 1} t h e n f i n d t h e v a l u e o f [\frac{a^{2} + a b + b^{2}}{a^{2} - a b + b^{2}}] i s : :$

A) 3/4	B) 4/3
C) 3/5	D) 5/3

Answer & Explanation Answer: B) 4/3

Explanation:

By simplifying, we get 4/3

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Filed Under: Square Roots and Cube Roots
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

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