Aptitude - Pipes and Cistern - Discussion

Discussion Forum : Pipes and Cistern - General Questions (Q.No. 4)
4.
Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
5 min.
9 min.
10 min.
15 min.
Answer: Option
Explanation:

Let B be turned off after x minutes. Then,

Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.

x 2 + 1 + (30 - x). 2 = 1
75 45 75

11x + (60 -2x) = 1
225 75

11x + 180 - 6x = 225.

x = 9.

Discussion:
90 comments Page 1 of 9.

Lakaka Levanduksu said:   11 months ago
Thanks @Anitha.
(2)

Charly said:   2 years ago
A = 75/2=>2/75,
B = 45=>1/45.

x(2/75+1/45) + (30-x)2/75 =1.
11x + 180-6x=225.
x = 9.
(5)

Anitha said:   2 years ago
A = 371/2
= 75/2 LCM of A & B(225) A=6, B=5
B=45.

Pipe is opened for 30 minutes so,
A * 30 = 6 * 30 = 180.

We need B's time,
Total time - A's time = 225 - 180.
= 45.
Time = C/E = 45/5.
=9 mins.
(56)

Guri said:   2 years ago
Good explanation. Thanks everyone.
(3)

Saradha said:   3 years ago
For this kind of question, Use formula (1 - full tank time / 2nd pipe time)* 1st pipe time.
Depends on the question what they are asking the 1st and 2nd times will be swapped. if 1st pipe time is asked the 1st pipe time should be outside like the above formula, or else 2nd one time should be outside.

Here full time is half an hr should be converted to min 1/2*60 = 30min.

Given data:
Full time = 30min.
1st pipe time= 37 * 1/2min => 37*2=74, 74+1= 75/2min.
2nd pipe time= 45min.

Apply formula
(1 - 30/75/2) * 45,
30 and 75 cancelled (1 - 6/15/2) * 45.

1 * 15/2 = 15/2 => 15/2 - 6 = 15-12/2 => 3/2.

(3/2 / 15/2)*45 remainders gets cancelled and remaining 3/15*45= 15 and 45 gets cancelled by 3 so 3 * 3 = 9min.

So, if u follow the above formula u can get the answer. You must be sure which is asked for if 1st one then outside the bracket if 2nd one then it should be outside.

Here b's time is asked so b's time is outside in the formula.
(13)

Subramanya said:   3 years ago
Well explained, Thanks @Nazmul.
(3)

NAZMUL HASAN APU said:   3 years ago
A's work in 1 hour = 2/75.
A's work in 30 minutes = (2/75) * 30 = 4/5.
Remaining work (1- 4/5) = 1/5.

B's work = (1/5) * 45 = 9 min.
(60)

Joel said:   3 years ago
Shortcut:

2/75 * 30 + x * 1/45 = 1,
x = 9 min.
(18)

Rekha said:   3 years ago
Well explained, Thanks @Ashwin.
(2)

Jothigonzi said:   3 years ago
@Abhijeet pol.

Nice and easiest explanation. Thanks.


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