Aptitude - Pipes and Cistern - Discussion
Discussion Forum : Pipes and Cistern - General Questions (Q.No. 14)
14.
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 and C are open for one hour each alternately, the tank will be full in:
Answer: Option
Explanation:
| (A + B)'s 1 hour's work = |  |
1 | + | 1 |  |
= | 9 | = | 3 | . |
| 12 | 15 | 60 | 20 |
| (A + C)'s hour's work = | |
1 | + | 1 | |
= | 8 | = | 2 | . |
| 12 | 20 | 60 | 15 |
| Part filled in 2 hrs = | |
3 | + | 2 | |
= | 17 | . |
| 20 | 15 | 60 |
| Part filled in 6 hrs = | |
3 x | 17 | |
= | 17 | . |
| 60 | 20 |
| Remaining part = | |
1 - | 17 | |
= | 3 | . |
| 20 | 20 |
| Now, it is the turn of A and B and | 3 | part is filled by A and B in 1 hour. |
| 20 |
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.
Discussion:
52 comments Page 2 of 6.
Hema said:
8 years ago
Taking the lcm(12,15,20) = 60 liters (capacity of the tank).
In 1 hr : A can fill 5 liters(60/12), B = 4 liters C = 3 liters.
Its given that A is open all time and B & C alternately.
So, in 1st hr : A+B = 9 liters.
2nd hr : A+C = 8 liters.
3rd hr : A+B = 9 liters.
4th hr : A+C = 8 liters.
5th hr : A+B = 9 liters.
6th hr : A+C = 8 liters.
7th hr : A+B = 9 liters.
Total = 60 liters (Capacity of the tank).
So Ans = C. 7 hours.
In 1 hr : A can fill 5 liters(60/12), B = 4 liters C = 3 liters.
Its given that A is open all time and B & C alternately.
So, in 1st hr : A+B = 9 liters.
2nd hr : A+C = 8 liters.
3rd hr : A+B = 9 liters.
4th hr : A+C = 8 liters.
5th hr : A+B = 9 liters.
6th hr : A+C = 8 liters.
7th hr : A+B = 9 liters.
Total = 60 liters (Capacity of the tank).
So Ans = C. 7 hours.
(1)
Govind said:
5 years ago
See......LCM of 12,15,20 is 60.
Therefore Total Tank Capacity is 60.
The individual capacity of A in One hour is 60/12=5.
The individual capacity of B in One hour is 60/15=4.
The individual capacity of C in One hour is 60/20=3.
A+B=5+4=9 in one hour.
A+C=5+3=8 in one Hour.
in two hours 17 liter. 17*3=51 liter in 6 hour and turns is A+B=9 in one Hour means.
6+1=7 Hour Final Answer.
Therefore Total Tank Capacity is 60.
The individual capacity of A in One hour is 60/12=5.
The individual capacity of B in One hour is 60/15=4.
The individual capacity of C in One hour is 60/20=3.
A+B=5+4=9 in one hour.
A+C=5+3=8 in one Hour.
in two hours 17 liter. 17*3=51 liter in 6 hour and turns is A+B=9 in one Hour means.
6+1=7 Hour Final Answer.
(27)
Anil said:
1 decade ago
First two hours 17/60 part tank filled.
We are taking every two hour calculation so after 6 hour 17/20.
If you consider next two hours means it will become 17/15 means tank is overflowing.
So only after 6 hour we calculating remaining part that is (1-17/20) = 3/20.
Now its A and B turn to fill the tank. It fill 3/20 part in one hour. So totally (6+1) = 7 hours.
We are taking every two hour calculation so after 6 hour 17/20.
If you consider next two hours means it will become 17/15 means tank is overflowing.
So only after 6 hour we calculating remaining part that is (1-17/20) = 3/20.
Now its A and B turn to fill the tank. It fill 3/20 part in one hour. So totally (6+1) = 7 hours.
Kumar Gourav said:
7 years ago
@All.
I believe its taken 6hrs straight after 2hrs because if all the three taps are kept open all the time, then it will take 5hrs to completely fill the tank. But, since in the question its given that B & C are opened alternatively every hour, that's why I guess it would take one hour more for the tank to be filled up.
I believe its taken 6hrs straight after 2hrs because if all the three taps are kept open all the time, then it will take 5hrs to completely fill the tank. But, since in the question its given that B & C are opened alternatively every hour, that's why I guess it would take one hour more for the tank to be filled up.
Kasinath @Hyd said:
1 decade ago
(A + B)'s 1 hour's work= 1/12+1/15 = 3/20.
(A + C)'s 1 hour's work =1/12+1/20 = 2/15.
Therefore (3/20 + 2/15)= 17/60 part of work is completed in first 2 hrs.
17/60 part of work completed in ------- 2hrs.
1 part (full work) completed in ------- x hrs.
Now cross multiply => x= 2(60/17) = 7hrs.
(A + C)'s 1 hour's work =1/12+1/20 = 2/15.
Therefore (3/20 + 2/15)= 17/60 part of work is completed in first 2 hrs.
17/60 part of work completed in ------- 2hrs.
1 part (full work) completed in ------- x hrs.
Now cross multiply => x= 2(60/17) = 7hrs.
Saisam said:
5 years ago
Suppose it takes "x" time for the complete tank to fill,so now tap"A" runs for all the time that is A*x whereas B and C runs alternatively so B*(x/2) &C*(x/2) respectively.
Therefore Ax +(B+C)*x/2=1.
That is x/12 +(1/15+1/20)*x/2=1.
Solving x, we get 7.
Therefore Ax +(B+C)*x/2=1.
That is x/12 +(1/15+1/20)*x/2=1.
Solving x, we get 7.
(6)
Ronak said:
8 years ago
As First A and B was started then after B is turned off and C is started so, After 6 hours ((A+C)+(A+B)+(A+C)) 17/20th part of the tank is filled when c is turned off now.
As given A+B fill the 3/20'th part in 1 hour so total 6+1 hours is the time taken to fill the Cistern.
As given A+B fill the 3/20'th part in 1 hour so total 6+1 hours is the time taken to fill the Cistern.
Sanjay said:
1 decade ago
Its very simple.
Part filled in 1st and 2nd hour:
1/12+1/15+1/12+1/20 = 17/60.
Part filled : Time taken
17/60 : 2 hr
1 : ?
By solving this we will get 6.8 that is nearby 7.
Part filled in 1st and 2nd hour:
1/12+1/15+1/12+1/20 = 17/60.
Part filled : Time taken
17/60 : 2 hr
1 : ?
By solving this we will get 6.8 that is nearby 7.
Piyush said:
9 years ago
Can I solve it in this way?
Let total time taken to fill the tank be x.
Now ,
(1/12)x + (1/15)(x/2) + (1/20)(x/2) = 1,
(x/12)+(x/30)+(x/40) = 1.
(10x+4x+3x)/120 = 1.
17x = 120.
x = 120/17.
x = 7(approx of 7.0588).
Let total time taken to fill the tank be x.
Now ,
(1/12)x + (1/15)(x/2) + (1/20)(x/2) = 1,
(x/12)+(x/30)+(x/40) = 1.
(10x+4x+3x)/120 = 1.
17x = 120.
x = 120/17.
x = 7(approx of 7.0588).
Vino said:
1 decade ago
Take LCM a, b, c = 180, tank capacity 180 liters.
a - 15 liter per hrs.
b - 12.
c - 9.
1hrs a+b = 27 liter.
1hrs a+c = 24 liter.
In choice more than 6 hrs.
= 27*4 = 108.
= 24*3 = 72.
Total 180 liters in 7 hrs.
a - 15 liter per hrs.
b - 12.
c - 9.
1hrs a+b = 27 liter.
1hrs a+c = 24 liter.
In choice more than 6 hrs.
= 27*4 = 108.
= 24*3 = 72.
Total 180 liters in 7 hrs.
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