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A tank is emptied everyday at a fixed time point. Immediately thereaft

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Bunuel
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A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   07 Apr 2020, 08:43
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A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

A. 4 : 12 PM
B. 4 : 24 PM
C. 4 : 36 PM
D. 4 : 46 PM
E. 4 : 48 PM


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A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   10 Apr 2020, 03:41
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Bunuel wrote:
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

A. 4 : 12 PM
B. 4 : 24 PM
C. 4 : 36 PM
D. 4 : 46 PM
E. 4 : 48 PM


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Solution:

If we let a be the number of hours it takes pump A to fill the tank by itself, then 1/a is the rate of pump A. Since pump B alone can fill the tank in 2 hours faster (6 pm vs. 8 pm), the number of hours it takes pump B to fill the tank by itself is (a - 2), and thus its rate is 1/(a - 2). Since on Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm to fill the tank, we can create the equation:

(a - 3) x 1/a + 2 x 1/(a - 2) = 1

(a - 3)/a + 2/(a - 2) = 1

Multiplying the equation by a(a - 2), we have:

(a - 3)(a - 2) + 2a = a(a - 2)

a^2 - 5a + 6 + 2a = a^2 - 2a

-3a + 6 = -2a

6 = a

Therefore, it takes pump A 6 hours to fill the tank by itself and pump B 4 hours to fill the tank by itself. Furthermore, the tank is filled starting at 2 pm. So on Thursday, if both pumps were used simultaneously at 2 pm, it will take 1/(⅙ + ¼) = 1/(4/24 + 6/24) = 1/(10/24) = 24/10 = 2.4 hours to fill the tank. Since 2.4 hours = 2 hours and 24 minutes, the tank will be filled at 4:24 pm.

Alternate Solution:

Let t be the number of hours it takes for pump B to fill the tank. Since pump A alone finishes filling the tank 2 hours later, compared pump B alone (6 pm vs. 8 pm), it takes pump A (t + 2) hours to fill the tank.

On Wednesday at 5 pm, pump A had 3 more hours to fill the entire tank; but pump B completed this job in only 2 hours. Thus, pump B works 3/2 faster compared to pump A or, equivalently, the time for pump A to fill the tank alone must be 3/2 of the time it takes for pump B to fill the tank. Since the time of pump A was t + 2 hours and the time of pump B was t hours, we can create the following equation:

t + 2 = 3t/2

2t + 4 = 3t

t = 4

Therefore, it takes pump B 4 hours to fill the tank by itself and pump A 4 + 2 = 6 hours to fill the tank by itself. Furthermore, the tank is filled starting at 2 pm. So on Thursday, if both pumps were used simultaneously at 2 pm, it took 1/(⅙ + ¼) = 1/(4/24 + 6/24) = 1/(10/24) = 24/10 = 2.4 hours to fill the tank. Since 2.4 hours = 2 hours and 24 minutes, the tank was filled at 4:24 pm.

Answer: B
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Re: A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   07 Apr 2020, 08:59
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Let pump A alone can fill the tank in t hours so time taken by pump B alone = t-2 hours
As per question , (t-3)/t+2/(t-2)=1
t^2-3t+6=t^2-2t
Or t=6
So the time at which pumps tank is emptied = 8 pm – 6 hours = 2 pm
Time taken by both pumps together to fill the tank =(6×4)/(6+4)=2.4 hours=2 hour 24 minutes
Thus tank will be filled by 2 pm + 2 hour 24 minutes=4:24 pm
correct answer B
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A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   07 Apr 2020, 09:06
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Bunuel wrote:
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

A. 4 : 12 PM
B. 4 : 24 PM
C. 4 : 36 PM
D. 4 : 46 PM
E. 4 : 48 PM


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Let, Time taken by A to fill tank = T
then, Time taken by B to fill tank = T-2

A's work of (T-3) hours + B's work of 2 Hours = 1 tank

i.e. A's 3 hours work = B's 2 hours work [difference is 1 between 3 and 2]-----(1)

But A's T hours' work = B's (T-2) hours' work [difference is 2 between T and T-2]---(2)

therefore multiplying eq.(1) by 2 both sides

i.e. A's 6 hours work = B's 4 hours work--- (3)

COmparing eq. (2) and eq(3)

T = 6 and T-2 = 4

i.e. A takes 6 hours and B takes 4 hours to fill the tank

A takes 6 hours and fills at 8 PM i.e. A starts 2 PM


A and B's one hour work together = (1/6)+(1/4) = 5/12

i.e. total time = 12/5 hours

Time of tank filling = 12/5 hours after 2:00 PM = 4:24 PM

Answer: Option B
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Re: A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   07 Apr 2020, 19:46
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took me a little time since we are dealing with arbitrary time and no rate
1=at
1=b(t-2)
1=a(t-3)+b(2)

a=1/t
b=1/(t-2)

1=1/t(t-3)+1/(t-2)(2)
1 = t-3/t+2/(t-2)
3/t=2/(t-2)
3t-6=2t
t=6

a=1/6
b=1/4

1=(1/6+1/4)t
t=12/5
2hr +2/5hr = 2hr 24min
B
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Re: A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   11 Apr 2020, 01:59
Bunuel wrote:
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

A. 4 : 12 PM
B. 4 : 24 PM
C. 4 : 36 PM
D. 4 : 46 PM
E. 4 : 48 PM


Are You Up For the Challenge: 700 Level Questions


Given:
1. A tank is emptied everyday at a fixed time point.
2. Immediately thereafter, either pump A or pump B or both start working until the tank is full.
3. On Monday, A alone completed filling the tank at 8 pm.
4. On Tuesday, B alone completed filling the tank at 6 pm.
5. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank.

Asked: At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

Let the time the tank is emptied everyday be x pm

Pump A fills the tank in (8-x) hours
Pump B fills the tank in (6-x) hours

(5-x)/(8-x) + 2/(6-x) = 1
1 - 3/(8-x) + 2/(6-x) = 1
(8-x)/3 = (6-x)/2
16 - 2x = 18 - 3x
x = 2 pm

Pump A fills the tank in (8-x) = 6 hours
Pump B fills the tank in (6-x) = 4 hours

At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

Work done in 1 hour if both pumps were used simultaneously all along
1/6 + 1/4 = 5/12

Tank will be filed in = 12/5 hours = 2.4 hours = 2 hours 24 mins

Time when the tank was filled on Thursday if both pumps were used simultaneously all along = 2:00 + 2:24 = 4:24 PM

IMO B
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Re: A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   23 Apr 2021, 03:42
preetamsaha wrote:
Let pump A alone can fill the tank in t hours so time taken by pump B alone = t-2 hours
As per question , (t-3)/t+2/(t-2)=1
t^2-3t+6=t^2-2t
Or t=6
So the time at which pumps tank is emptied = 8 pm – 6 hours = 2 pm
Time taken by both pumps together to fill the tank =(6×4)/(6+4)=2.4 hours=2 hour 24 minutes
Thus tank will be filled by 2 pm + 2 hour 24 minutes=4:24 pm
correct answer B

------------------------------
Why are we taking (t-2) for B?
Where did (t-3) come from?

Could you please explain this again?
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Re: A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   25 Apr 2021, 11:27
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Bunuel wrote:
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

A. 4 : 12 PM
B. 4 : 24 PM
C. 4 : 36 PM
D. 4 : 46 PM
E. 4 : 48 PM


Are You Up For the Challenge: 700 Level Questions



1: A works till 8 pm
2. B works till 6 pm
3. A works till 5 pm and B till 7 pm
4. A and B work till ? pm

From 1 and 3:
1: A works till 5 pm and A till 8 pm
3. A works till 5 pm and B till 7 pm
Both do the same work
So, cancelling A's work till 5 pm:
3 hours of A = 2 hours of B
=> A : B (efficiency) = 2 : 3

From 2 and 3:
2. B works till 6 pm
3. A works till 5 pm and B till 7 pm
Removing B's common work of 2 hours from both:
B's work till 4 pm = A's work till 5 pm

// We can say that there is a difference of 1 here and also above where we got 3 hours of A = 2 hours of B
Thus, starting time of filling must be 2 pm to ensure the efficiency ratio 2:3

// Alternatively: assuming starting time as X pm:

B's work till 4 pm = A's work till 5 pm and efficiency ratio of a:B = 2:3, we have:
(4-X)/(5-X) = 2/3 => X = 2

Thus, filling starts at 2 pm

So, A takes 8-2 = 6 hours
B takes 6-2 = 4 hours

A and B together take = 6*4/(6+4) = 2.4 hrs = 2 hours 24 min from 2 pm
i.e. 4:24 pm

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Re: A tank is emptied everyday at a fixed time point. Immediately thereaft [#permalink] New post   14 Sep 2022, 13:37
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