Aptitude - Pipes and Cistern - Discussion

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.

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.

L.C.M of 40 and 60 is 120.

So A's rate of work is 2 and B's rate of work is 3.

Hence now B work for half of time an A+B for another half.

So, 3x+(2x3)x = 120.

Hence x = 15 which is half time hence full time is 2x = 2x15 = 30 min.

@Vinayak.

How will you multiply (2*3) you need to add them?

1st tape can fill half of the tank in 3 hours.

Remaining part = 1-1/2 = 1/2 part.

Now 4 tape can fill the tank in 1 hour = 4*1/6 = 2/3.

Now,
2/3 parts fill in 1 hour.
1/2 parts fill in 1*3/2*2 = 45 mins.

So, total time = 3hrs+45mins = 3 hours 45 mins.

Why can't it be In logical manner?

Half time of B + half of the time of (A + B) ==> 20+ (A+B) filling time.

A + B in 1 min = 1/24.

In x min = x/24 ==> 1/2 of Total Volume V.

So x = 12; Total time = 20 + 12 = 32.

By LCM method answer is 32.
A B A+B
60 40 24 ---> Time.
2 3 5(3+2) ---> lit/min.
___ ___ _____
120 120 120 ---> capacity

For 60 lit, B will continue so it will take 20min.
And remaining 60 lit both A+B will work i.e will take 12min.
Total time = 20 + 12 = 32min.

@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.

When you consider half the volume the answer is 32. But when you consider half the time the answer is 30.

A's 1 minute work = 1/60.
B's 1 minute work = 1/40.

half d work done by B and remaining Half work by A&B.
= 1/2 [1/40] + 1/2 [1/24] {because 1/60+1/40=1/24}.
= 1/30.

Work done in 30 min.