Aptitude - Pipes and Cistern - Discussion

@Sri, if we try by the method of LCM the answer is 32 only.

Explained as,

A takes 60 mins
B takes 40 mins
taking LCM of both 60 and we get 120.

Considering 120 to be the capacity of the tank.

Now A fills the 120/60 = 2 units/min
B fills 120/40 = 3 units/min.
Combined A and B fill 3+2 = 5 units per min.

Now half of the units is filled by B alone i.e 120/2 = 60 units (half of capacity calculated by taking the LCM).

Therefore, the time taken by B alone is 60/3.

(calculations
3 units = 1 min
1 unit = 1/3 mins
60 units = 60/3 = 20 mins)

So B alone takes 20 mins.

Now for other half,

A and B together fills remaining 60 units.
A and B together fills 3+2 units/min = 5 units/min

(calculation
A+B fills 5 units in 1 min
they fill 1 unit in 1/5 min
further, they fill 60 units in 60/5 = 12 mins)

Therefore they take time = B alone time + time taken by A and B Combined = 20 + 12 mins = 32 mins.

Given :
A = 1/60 min
B = 1/40 min.

B works alone half time means 1/2, no confusion, put x/2.
A and B both work together that also one half puts another x/2.

Step 1 :
First, we do B alone in one half the value is ×/2 and the actual time of B is 1/40, so, x/2×1/40 = ×/80.
B half value = x/80.

Step 2 :
A and B work, take lcm of 60,40 = 120.
It looks like 2/120 + 3/120 = 5/120 => 1/24.
Then implement the A and B work half x/2 × 1/24 = x/48.
A and B work half value = x/48.

Step 3 :
Adding your half's answers B half = x/80 and A&B half = x/48.
Total work done = 1,
So, x/80 + x/48 =1,
Take lcm on both sides, don't forget to take lcm, lcm of 80,48 = 240
3x/120 + 5x/240 = 8x/240 = 1.

Then simplify,
8x/240 = 1.
x = 240/8 => 30 minutes.

A simple method for solving this problem without formula :

Firstly, For a 1/2 Minute i.e half-minute Pipe B is used so,

1    1     1
-  * -   = -
2    40    80

Now, remaining part of tank should be filled by both A and B in remaining 1/2 i.e half minute.

For which combined capacity of A and B have to used as both are working simultaneously.

1     [  1     1   ]     1
-  *  [  -  +  -   ]  =  -
2     [  40    80  ]     48

Finally,
We have to add tank filled by B alone and A+B together.

1    1      128
-  + -   =  ---
80   48     3840

    1
 =  -
    30

So, required answer is 30 mins respectively.

Mine answer is coming 32 mins. By LCM method I am getting different answer.

A = 60 min.

B = 40 min.

By taking LCM total work is 120 unit. (say litre).

So a fills the tank in 120/60 = 2 litre/min.

B does it in 120/40 = 3 litre/min.

Together 5 litres. So time taken by both a and b to complete work is 120/5 = 24 min.

Now half tank means capacity of 60 litres. (60+60=120).

Now half the tank is filled by a+b=60/ (3+2) =12 min.

And half the tank is filled by b only = 60/3=20 min.

So therefore, 12+20=32 min.

LCM(60,40) = 120.
Suppose the capacity of the tanker is 120litre.
Then, the quantity filled by pipe A in 1 min=120/60= 2 litres.
The quantity filled by pipe B in 1 min=120/40=3 litre.

The quantity filled by pipe A and B together in 1 min= 2 + 3 = 5 litre.

Suppose the tanker is filled in x minutes.

Then, to fill the tanker from the empty state, B is used for x/2 minutes and A &B together is used for the rest x/2 minutes.

3x/2 + 5x/2 = 120;
x/2(3+5) = 120;
8x/2 = 120
X = 30.

Required time =30 minutes.

By LCM method I am getting different answer.

A = 60 min.
B = 40 min.

By taking LCM total work is 120 unit.

So A does 120/60 = 2 unit.

B does 120/40 = 3 unit.

Together 5 unit so time taken by both A and B to complete work is 120/5 = 24 min.

It means B will work alone for 12 min and work done by B is 12x3 = 36 unit.

Remaining work is 120-36 = 84 unit which is done by both A and B so 84/5 = 16.8 min.

Then total time taken is = 12+16.8 = 28.8 min.

Cross-check:

TA = 60 min.
TB = 40 min.
As per the given statement, A and B run together for 15 min (=Answer/2=30/2), and B runs alone for the next 15 mins (=Answer/2=30/2).
P1 = Part filled by first 15 min = 15*(1/TA+1/TB) = 15*(1/60+1/40) = 15*5/120=5/8.
P2 = Part filled by next 15 min = 15*(1/TB) = 15*(1/40) = 3/8.
Full tank = summation of both parts = P1+P2 = 5/8+3/8 = 1.
Hence it is proved that the given explanation is correct.

A = 60 min.
B = 40 min.

Total work= 120.

The capacity of A and B is 2 and 3 respectively.

In Q, is clear that B is used for half the time, so we will take 20 min.

So, in 20 min B will fill = 60 work.
Remaining work = 60.
Now, both A and B is used for other half means is clear that for other half work that is 60.

So the capacity of A+B=5.

Time = 60/5 = 12 min.
Total time = 20 + 12 = 32 min.

Its very simple if we calculate as follows,

Total work done by A+B in 1 minute=1/40+1/60 = 1/24.

Total work done by B alone in 1 minute = 1/40.

1/2 work done by A+B in 1 minute = 1/24*1/2 = 1/48.

1/2 work done by B alone in 1 minute = 1/40*1/2 = 1/80.

Total 1/2 work done by (A+B) and B in 1 minute = 1/80+1/48 = 8/240 = 1/30.

So the total work done by 1/2(A+B) and 1/2B = 30 minutes.

LCM of 60 and 40 is 120.(total work=120).
So the efficiencies are 2 and 3.
A:B=2:3.

A+B=5 (combined efficiency).
Then consider the total time required to fill the tank as X.
B is used for half of the time and then A and B fill it together for the other half.then we can write as,
(X/2) x 5 + (X/2) x 3 = 120.
By solving this equation you will get X = 30.