Aptitude - Pipes and Cistern - Discussion

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.

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.

Shortcut:

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

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.

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.

We get total amount to be filled by taking the LCM of (45,75/2) = 225litres.
Efficiency of A=225/(75/2)= 6litres/min
Efficiency of B=225/(45) = 5litres/min
So A in 30mins =30* 6 = 180litres
Remaining amount = 225 - 180 = 45L
Now B fills 5L in 1min,
45L it requires 9mins.

Good explanation. Thanks everyone.

Thanks @Anitha.

Well explained, Thanks @Nazmul.

Well explained, Thanks @Ashwin.