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 3 of 6.
Gnanamayil.k said:
1 decade ago
I feel its all lengthy calculation. Is there any simple shortcut method?
Potato singh said:
1 decade ago
Yes, take a bucket of 60 ltr capacity. Install 3 taps in your bathroom and get started.
Arun said:
1 decade ago
1 hr tank can fill 3/20 -> (1/12+1/15).
2nd hr tank can fill 3/20+2/15 = 17/60.
For 2 hr it fills 17/60 then for 1 hr it fills 17/120 -> (1/2*17/60).
Consider 17 table 17*6 = 102, so in six hours it it fills 102/120 and next hr B Pipe will be open and.
Fills as 102/120+3/20 = 1. So 7 hrs it will take.
Another way:
For 2 hrs it fills 17/60.
Consider next 2 hrs i.e. 4 hrs 2*17/60 = 34/60.
Consider next 2 hrs i.e 6 hrs 51/60 only 9 is less for 60 i.e to full.
So next 1 hr b pipe open 51/60+9/60 = 1.
2nd hr tank can fill 3/20+2/15 = 17/60.
For 2 hr it fills 17/60 then for 1 hr it fills 17/120 -> (1/2*17/60).
Consider 17 table 17*6 = 102, so in six hours it it fills 102/120 and next hr B Pipe will be open and.
Fills as 102/120+3/20 = 1. So 7 hrs it will take.
Another way:
For 2 hrs it fills 17/60.
Consider next 2 hrs i.e. 4 hrs 2*17/60 = 34/60.
Consider next 2 hrs i.e 6 hrs 51/60 only 9 is less for 60 i.e to full.
So next 1 hr b pipe open 51/60+9/60 = 1.
Swetha said:
10 years ago
Please say short cut method for problem 14 it is length process.
Narendra said:
10 years ago
Let's assume B works for x hours and C for y hours. So A will be working for x+y hours.
= (x+y)/12 + x/15 + y/20 = 1 (tank having 1 part).
= 9x + 8y = 60.
x = 4; y = 3.
= (x+y)/12 + x/15 + y/20 = 1 (tank having 1 part).
= 9x + 8y = 60.
x = 4; y = 3.
Brajesh said:
9 years ago
It was a nice solution @Alvin .
Thank you.
Thank you.
INNA REDDY CHILAKALA said:
9 years ago
@Anil.
Your method is simple and easy to solve the solution.
Thank you.
Your method is simple and easy to solve the solution.
Thank you.
Siva said:
9 years ago
Thank you, @Alvin.
Your method is easy and really simple.
Your method is easy and really simple.
Sadam said:
9 years ago
x/12 + (1/15 + 1/20) x/2 = 1.
x = 7 hours.
x = 7 hours.
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).
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers