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Monday, 29 April 2019

MATHS SOLVED IN STEPS: Pipe and Cisterns - 04

31. 13 buckets of water fill a tank when the capacity of each bucket is 51 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 17 litres?
A. 33                            B.  29
C. 39                            D.  42
Answer: Option C
Explanation:
Capacity of the tank = (13 x 51) litre
Number of buckets required of capacity of each bucket is 17 litre = (13x51)/17
=13x3=39


32.  Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
A. 2.4  hr                    B.  3 hr
C. 4 hr                         D.  4.2 hr
Answer : Option A
 Explanation :
Part filled by pipe A in 1 hour = 1/8 Part filled by pipe B in 1 hour = ¼
Part filled by pipe C in 1 hour = 1/24
Part filled by pipe A, pipe B and pipe C in 1 hour
= 1/8+1/4+1/24=10/24
i.e, pipe A, pipe B and pipe C together can fill the tank in 24/10 hours = 2.4 hours

33. Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the taps are opened simultaneously, and the tap A is closed after 3 minutes, then how much more time will it take to fill the tank by tap B?
A. 6 min 15 sec B. 5 min 45 sec
C. 5 min 15 sec D. 6 min 30 sec
Answer : Option B
Explanation :
Part filled by pipe             A         in        1         minute = 1/8
Part filled by pipe             B         in        1         minute = 1/14
Part filled by pipe A and pipe B in 1 minute = (1/8)+(1/14)=11/56
Pipe A and pipe B were open for 3 minutes Part filled by pipe A and pipe B in 3 minutes = 3x(11/56)
=33/56
Remaining part = 1-(33/56) =23/56
Time taken by pipe B to fill this remaining part = (23/56) + (1/14)
=(23x14) + 56=23/4 minutes = 5 minutes 45 seconds


34. A water tank is two-fifth full. Pipe A can fill a tank in 12 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. 2.8 min                  B. 4.2 min
C. 4.8 min                  D. 5.6 min
Answer : Option C
Explanation :
Since pipe B is faster than pipe A, the tank will be emptied.
Part filled by pipe A in 1 minute = 1/12
Part emptied by pipe B in 1 minute = 1/6
 Net part emptied by pipe A and pipe B in 1 minute = 1/6-1/12 =1/12
Time taken to empty 2/5 of the tank = (2/5) + (1/12)
=(2x12)+5=4.8 min

35. Pipes A and B can fill a tank in 8 and 24 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
A. 18 hr                      B. 6 hr
C. 24 hr                       D. 12 hr
Answer: Option D
Explanation :
Part filled by pipe A in 1 minute = 1/8
Part filled by pipe B in 1 minute = 1/24
Part emptied by pipe C in 1 minute = 1/12
Net part filled by pipe A, pipe B and pipe C in 1 minute
= (1/8)+(1/24)-(1/12)
=2/24
=1/12
i.e, the tank will be filled in 12minutes

36. One pipe can fill a tank 6 times as fast as another pipe. If together the two pipes can fill the tank in 22 minutes, then the slower pipe alone will be able to fill the tank in:”
A. 164 min B. 154 min C. 134 min D. 144 min
Answer : Option B
Explanation :
Let the slower pipe alone can fill the tank in x minutes. Then the faster pipe can fill the tank in 6 x minutes
 Part filled by the slower pipe in 1 minute = 1/x
Part filled by the faster pipe in 1 minute = 6/x
Part filled by both the pipes in 1 minute = 1/x+6/x
It is given that both the pipes together can fill the tank in 22 minuts
Part filled by both the pipes in 1 minute = 1/22
1/x+6/x=1/22 7=(1/22)x x=22x7=154
i.e.,the slower pipe alone fill the tank in 154 minutes


37. Two pipes A and B can fill a tank in 2 and 6 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A. 3 min                      B. 2.5 min
C. 2 min                      D. 1.5 min
Answer : Option D
Explanation :
Part filled by the first pipe in 1 minute = 1/2
Part filled by the second pipe in 1 minute = 1/6
Net part filled by pipe A and pipe B in 1 minute = (1/2)+(1/6)=2/3
i.e, pipe A and B together can fill the tank in 3/2 minutes = 1.5 minutes
* MATHS (SOLVED IN STEPS ==> Ratio and Proportion
* MATHS (SOLVED IN STEPS ==> Progressions
* MATHS (SOLVED IN STEPS ==> Percentage
* MATHS (SOLVED IN STEPS ==> Surds and Indices
* MATHS (SOLVED IN STEPS ==> Calendar
* MATHS (SOLVED IN STEPS ==> Square and cube
* MATHS (SOLVED IN STEPS ==> Simplification
* MATHS (SOLVED IN STEPS ==> Problems on Average
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> Profit and Loss
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Problems on Age 
* MATHS (SOLVED IN STEPS ==> ODD MAN
* MATHS (SOLVED IN STEPS ==> TIME & WORK



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