1. Two pipes P and Q can fill the tank in 900 and 100 hours respectively. If they are opened together, then in how many hours will the tank be filled?
दो पाइप P और Q एक टंकी को क्रमशः 900 और 100 घंटे में भर सकते हैं। यदि उन्हें एक साथ खोला जाता है, तो टंकी कितने घंटों में भर जाएगी?
Option “D” is correct.
P alone can fill a tank = 900 hours
P’s one-hour work = 1/900
Q alone can fill a tank = 100 hours
Q’s one-hour work = 1/100
When they are opened together,
P + Q = (1/900) + (1/100)
⇒ (1 + 9)/900
⇒ (10/900) = 1/90
Hence, when both the pipes are opened together, the whole tank will be filled in 90 hours.
2. Two pipes, A and B can fill an empty cistern in 20 min and 40 min, respectively. Both the pipes are opened together, and after some time, pipe A is closed. If the cistern gets filled in 30 min, then for how long was pipe A kept open?
दो नल A और B एक खाली टंकी को क्रमशः 20 मिनट और 40 मिनट में भर सकते हैं। दोनों नलों को एकसाथ खोला जाता है, और कुछ समय के बाद नल A बंद कर दिया जाता है। यदि टंकी 30 मिनट में भर जाती है, तब नल A कितने समय के लिए खोला गया था?
Option “A” is correct.
Given:
Pipe A can fill the cistern in 20 min
Pipe B can fill the cistern in 40 min
Cistern gets filed in 30 min
Calculation:
As we know the efficiency is inversely proportional to the time.
Efficiency of pipe A and B = 40 : 20 = 2 : 1
Suppose the total work = 40 units
Suppose the pipe A was opened for x min.
According to the question
⇒ 2x + 1 × 30 = 40
⇒ x = 10/2 = 5 min
∴ A can fill the cistern in 5 min
Alternate Method
The cistern filled by Pipe B in 30 min = 30/40 = 3/4
Remaining tank = 1 – 3/4 = 1/4
This 1/4 part of cistern is filled by A
A was opened for 20/4 = 5 min
∴ A can fill the cistern in 5 min
3. An inlet pipe can fill a tank in 10 hours and an outlet pipe can empty the completely filled tank in 20 hours. Both the pipes are opened at 6.30 a.m. When will the tank get filled?
एक भरने वाला नल एक टंकी को 10 घंटे में भर सकता है और एक निकासी नल पुर्णतः भरी हुई टंकी को 20 घंटे में खाली कर सकता है। दोनों नलों को पूर्वाह्न 6.30 बजे खोला जाता है। टंकी कब भर जाएगी?
Option “D” is correct.
Given:
An inlet pipe can fill the tank in 10 hours
An outlet pipe can empty the tank in 20 hours
Both pipes are opened at 6.30 a.m
Formula used:
Work done = Time × Efficiency
Calculation:
Let the capacity of the tank be 20 units.
(∵ LCM of 10 and 20 is 20)
Efficiency of inlet pipe = 20/10 = 2
Efficiency of outlet pipe = -20/20 = -1
1 hour work of both pipe = 2 – 1 = 1
Time taken to filled the tank = 20/1 = 20 hours
Time = 6.30 am + 20 = 2.30 a.m. next day
∴ The tank will be filled by 2.30 a.m next day
4. The ratio of efficiency of pipe A, B and C is 5 ∶ 7 ∶ 3. Altogether three pipes fill the tank in 20 hrs. A and B are inlet pipes and C is an outlet pipe. If A and C open for 13 hrs, in how many hours pipe B alone fill the remaining tank?
पाइप A, B और C की दक्षता का अनुपात 5 ∶ 7 ∶ 3 है। एक साथ मिलकर तीनों पाइप टंकी को 20 घंटे में भरते हैं। A और B भरने वाला पाइप हैं तथा C निकासी पाइप है। यदि A और C को 13 घंटों के लिए खोला जाता है, तो कितने घंटों में पाइप B शेष टंकी को भर देगा?
Option “A” is correct.
Efficiency ratio of pipe A, B and C = 5 ∶ 7 ∶ 3
As we know, Pipe A and Pipe B are inlet pipe and Pipe C outlet pipe, then
Total work = (5 + 7 – 3) × 20 = 180
Tank filled by A and C in 13 hrs = (5 – 3) × 13 = 26
Remaining work = 180 – 26 = 154
Pipe B alone fill the remaining tank = 154/7 = 22 hrs
5. Both tap M and tap N together can fill a tank in 20/3 hours. If tap M opens for only 4 hours and the remaining tank fills by tap N for only 9 hours. How many hours to fill the tank by tap N?
नल M और नल N दोनों एक साथ 20/3 घंटे में एक टैंक भर सकते हैं। यदि नल M केवल 4 घंटे कार्य करता है, और शेष टैंक नल N केवल 9 घंटे में भरता है। नल N द्वारा टैंक को भरने में कितने घंटे लगेंगे?
Option “B” is correct.
Calculation:
According to question
⇒ (M + N) × 20/3 = 4M + 9N
⇒ 20M + 20N = 12M + 27N
⇒ 8M = 7N
⇒ M/N = 7/8
To fill the complete tank by tap N = (4M + 9N)/efficiency of N
To fill the complete tank by tap N = (4 × 7 + 9 × 8)/8 = 100/8 = 25/2
∴ To fill the complete tank by tap N is 12.5 hours
6. Pipe A can fill a tank in 36 minutes and Pipe B can empty the tank in 45 minutes. If both the pipes are opened simultaneously, then find the time (in hours) to fill the tank to half its capacity.
पाइप A, 36 मिनट में एक टैंक भर सकता है और पाइप B 45 मिनट में टैंक खाली कर सकता है। यदि दोनों पाइप एक साथ खोले जाते हैं, तो टैंक के आधे हिस्से को भरने के लिए लगनेवाला समय (घंटों में) ज्ञात कीजिए।
Option “B” is correct.
Concept used:
Efficiency = Total Work/ Total Time
Calculation:
Let the total capacity of tank = 180 unit [LCM of 36 and 45]
According to the question
Efficiency of Pipe A = 180/35 = 5
Efficieny of Pipe B = -180/(45) = -4 [B is an outlet pipe]
Combined efficiency of (A + B) = 5 + (-4) = 1
So, Time taken by (A + B) to fill the tank = 180/1 = 180 minutes
So, Time taken by (A + B) to fill half tank = 180/2 = 90 minutes.
Alternate Method
According to question,
In 1 minute pipe A can fill 1/36 part of the tank
And in 1 minute pipe B can empty 1/45 part of the tank
⇒ Work done by pipe (A + B) in 1 minute is (1/36 – 1/45)
⇒ In 1 minute pipe (A + B) can fill 1/180 part of tank
⇒ The time taken by pipe (A + B) to fill the full tank is 180 minutes
So, time taken by pipes (A + B) to fill half of the tank is 90 minutes
∴ Time taken by pipes (A + B) to fill half of the tank is 1.5 hours
7.A water tank is filled in 5 hours by three pipes X, Y and Z the pipe Z is thrice as fast as Y and Y is twice as fast as X. How much time will pipe X alone take to fill the water tank?
एक पानी की टंकी तीन पाइप X, Y और Z से 5 घंटे में भर जाता है, पाइप Z, पाइप Y की तुलना में तीन गुना अधिक तीव्र है और पाइप Y, पाइप X की युलना में दो गुना अधिक तीव्र है। अकेला पाइप X पानी की टंकी को भरने में कितना समय लेगा?
Option “B” is correct.
Short Trick:
Time taken by X alone = 5 × (1 + 2 + 6)/1 = 45 hours
Detailed Solution:
Let, in 1 hour X can fill = a lit
∴ In 1 hour Y can fill = 2a lit
∴ In 1 hour Z can fill = 6a lit
∴ Capacity of the tank = 5(a + 2a + 6a) = 45a lit
Let, X alone can fill the tank in t hours
According to the question,
⇒ t × a = 45a
⇒ t = 45
∴ X alone can fill the tank in = 45 hours
8. Three pipes A, B, and C can fill a tank in 10 minutes, 12 minutes, and 15 minutes respectively. The pipe B is closed 3/2 minutes before the tank is filled. In what time the tank will full?
तीन पाइप A, B और C एक टंकी को क्रमशः 10 मिनट, 12 मिनट और 15 मिनट में भर सकते हैं। पाइप B को टंकी के भर जाने से 3/2 मिनट पहले बंद कर दिया जाता है। टंकी कितने समय में भर जाता है?
Option “C” is correct.
Let the capacity of the tank be 60 units (LCM of 10, 12 ,and 15 = 60)
Efficiency, A = 60/10 = 6 units/min, B = 60/12 = 5 units/min, C = 60/15 = 4 units/min
Pipe B is closed 3/2 min before the tank fill
⇒ (A + C) work for 3/2 min extra
Tank filled in 3/2 min = 10 × 3/2 = 15 unit
⇒ Remaining part of tank = 60 – 15 = 45 unit
This is filled by all three pipes
⇒ Time taken to fill 45 units = 45/15 = 3 minute
∴ Total time taken by pipes to fill the tank = 3 min + 1.5 min = 4.5 min
9. Two taps can fill an empty cistern in 8 min and 20 min, respectively. However, together, they take 30 min to fill it because of a leak. How much time will the leak take to empty a full cistern?
दो नल एक खाली टंकी को क्रमशः 8 मिनट और 20 मिनट में भर सकती है। हालाँकि, छिद्र के कारण वे भरने में 30 मिनट लेते हैं। तो एक भरी हुई टंकी को खाली करने में छिद्र कितना समय लेगा?
Option “C” is correct.
Given:
Time taken by each tap alone to fill the tank = 8 min and 20 min
Time taken by both taps to fill with a leak = 30 min
Formula Used:
Total work = Efficiency × Time taken
Calculation:
Let, the leak will take x minutes to empty a full cistern
According to the question,
1/8 + 1/20 – 1/x = 1/30
⇒ 1/x = 1/8 + 1/20 – 1/30
⇒ 1/x = (15 + 6 – 4)/120
⇒ 1/x = 17/120
⇒ x = 120/17
∴ The leak will take 120/17 min to empty a full cistern
10. A tank has two inlets and an outlet. The inlets fill up the tank in 6 hours and 8 hours individually and outlet empties it in 10 hours. If the inlets are opened for an hour and closed and then all the three taps are opened together, how much time will it take to fill up remaining tank?
एक टंकी में दो प्रवेशद्वार और एक बहिर्द्वार है। प्रवेशद्वार टंकी को व्यक्तिगत रूप से 6 घंटे और 8 घंटे में भर देता हैं और बहिर्द्वार इसे 10 घंटे में खाली कर देता है। यदि प्रवेशद्वार एक घंटे के लिए खोले जाते हैं और बंद कर दिए जाते हैं और फिर तीनों नलों एक साथ खोला जाता हैं, तो शेष टंकी को भरने में कितना समय लगेगा?
Option “C” is correct.
GIVEN:
Two inlets can fill the tank in 6 hours and 8 hours respectively.
Outlet pipe can empty the tank in 10 hours.
CALCULATION:
Two inlets can fill the tank in 6 hours and 8 hours respectively.
⇒ Quantity of tank filled by inlet pipes in 1 hour = 1/6 + 1/8 = 7/24 units
After 1 hour all the three pipe are opened then tank filled = 1/6 + 1/8 – 1/10 = 23/120 units
Total work done by all the three pipe = 1 unit
Let the remaining tank be filled in x hours.
⇒ 7/24 + x × 23/120 = 1
⇒ x = 85/23
∴ Time taken to fill the remaining tank = 85/23 hours
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