Aptitude - Pipes and Cistern - Discussion
Discussion Forum : Pipes and Cistern - General Questions (Q.No. 12)
12.
A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Answer: Option
Explanation:
| Part filled by (A + B) in 1 minute = |  |
1 | + | 1 |  |
= | 1 | . |
| 60 | 40 | 24 |
Suppose the tank is filled in x minutes.
| Then, | x | |
1 | + | 1 | |
= 1 |
| 2 | 24 | 40 |
 |
x | x | 1 | = 1 |
| 2 | 15 |
x = 30 min.
Discussion:
51 comments Page 2 of 6.
Chinmay said:
7 years ago
Question is asked in terms of time, not volume (work). So, 30 mins is the answer. LCM method assumes half volume not half time.
(1)
Praneeth Reddy said:
8 years ago
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.
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.
(1)
Siddhesh said:
8 years ago
(A+B) & B are not working simultaneously, one of them assume B first work for say x minutes and fill some part of tank.
According to question other (A+B) also work for x minute to fill the remaining part.
The part filled by B in x minutes = x/40,
part filled by (A+B) in x minutes.
= x/24
(x/40) + (x/24)=1
x =15
So total time is 2x = 30 min.
According to question other (A+B) also work for x minute to fill the remaining part.
The part filled by B in x minutes = x/40,
part filled by (A+B) in x minutes.
= x/24
(x/40) + (x/24)=1
x =15
So total time is 2x = 30 min.
(1)
VAISHNAVI.N said:
1 decade ago
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.
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.
(1)
Emon said:
8 years ago
Check the question. It is said half the time. So the answer is 30.
If it is said half of the tanker then the answer would be 32.
If it is said half of the tanker then the answer would be 32.
(1)
Rohit said:
8 years ago
LCM of 60 and 40 is 120.
So a 1 min work is 120/60=2.
And b 1 min work is 120/40=3.
After getting 1 min work by LCM as A=2 and b=3..consider full time as x so the halftime will be x/2.
So,
3x/2 + (2+3)x/2=120...solving it u get x=30.
Here 120 is taken on right because it's the total quantity.
So a 1 min work is 120/60=2.
And b 1 min work is 120/40=3.
After getting 1 min work by LCM as A=2 and b=3..consider full time as x so the halftime will be x/2.
So,
3x/2 + (2+3)x/2=120...solving it u get x=30.
Here 120 is taken on right because it's the total quantity.
(1)
Santosh said:
7 years ago
The answer is 32. I agree with this.
(1)
Soham said:
7 years ago
The answer is wrong.
The question didn't ask, they did in halftime, the question asked they did the half work. So let's solve it simple way.
40 minty tea for full work for B, so 20 minutes for half work for B.
24 minutes for both AandB, so 12 minutes for half work for B.
SO TOTAL TIME TAKEN IS 20+12=32 minutes, 30 is wrong answer.
The question didn't ask, they did in halftime, the question asked they did the half work. So let's solve it simple way.
40 minty tea for full work for B, so 20 minutes for half work for B.
24 minutes for both AandB, so 12 minutes for half work for B.
SO TOTAL TIME TAKEN IS 20+12=32 minutes, 30 is wrong answer.
(1)
Pavan said:
7 years ago
Very good explanation, Thank you @Ishan.
(1)
Shankar said:
9 years ago
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.
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.
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