In this focused guide, we delve into the core concepts of Time and Work, Work and Wages, and Pipe and Cistern problems. By offering concise solutions, we aim to equip you with efficient problem-solving techniques for these vital areas of quantitative aptitude.
Assignment-1
Que 1: 4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?
(a) 22(2/7) days
(b) 25(1/2) days
(c) 5(1/7) days
(d) 12(7/22) days
Solution: 4M+3W⇒6
5M+7W⇒4
24M+18W=20M+28W
4M=10W
M:W=5:2 (M+W=7 unit)
Total work= 24×5+18×2= 120+36=156 unit
Required time= 156/7= 22(2/7) days
Option (a) is correct.
Que 2: If 8 boys and 12 women can do a piece of work in 25 days, in how many days can the work be done by 2 boys and 3 women working together?
(a) 96 days
(b) 100 days
(c) 80 days
(d) Cannot be determined
Solution: 8B+12W : 2B+3W= 4:1
4×25=1×t
t=100 days
Option (b) is correct.
Que 3: Arun and Vinay together can do a piece of work in 7 days. If Arun does twice as much work as Vinay in a given time, how long will Arun alone take to do the work.
(a) 6.33 days
(b) 10.5 days
(c) 11 days
(d) 72 days
Solution: A+V⇒7
A=2 unit/day
V=1 unit/day
Total work= (2+1)×7=21 unit
Required time for Arun= 21/2=10.5 days
Option (b) is correct.
Que 4: Raju can do a piece of work in 10 days, Vicky in 12 days and Tinku in 15 days. They all start the work together, but Raju leaves after 2 days and Vicky leaves 3 days before the work is completed. In how many days is the work completed?
(a) 5 days
(b) 6 days
(c) 7 days
(d) 8 days
Solution: R⇒10, V⇒12, T⇒15
Efficiency= 6:5:4
Total work= 60 unit
6×2+5×(t-3)+4×t=60
t=7 days
Option (c) is correct.
Que 5: Apurva can do a piece of work in 12 days. Apurva and Amit completed the work together and were paid 54 ₹ and 81 ₹ respectively. How many days must they have taken to complete the work together?
(a) 4 days
(b) 4.5 days
(c) 4.8 days
(d) 5 days
Solution: Apurva: Amit= 54: 81= 2:3
Total work= 2×12= 24 unit
Required time= 24/5= 4.8 days
Option (c) is correct.
Que 6: Ajay and Vijay undertake to do a piece of work for 200. Ajay alone can do it in 24 days while Vijay alone can do it in 30 days. With the help of Pradeep, they finish the work in 12 days. How much should Pradeep get for his work?
(a) 20 ₹
(b) 100 ₹
(c) 180 ₹
(d) 50 ₹
Solution: A⇒24 days
V⇒ 30 days
A+V+P⇒ 12 days
Ratio of efficiencies= 5:4:10
A:V:P= 5:4:1
Pradeep’s income= 200×1/10= 20 ₹
Option (a) is correct.
Que 7: Ajay, Vijay and Sanjay are employed to do a piece of work for 529 ₹. Ajay and Vijay together are supposed to do 19/23 of the work and Vijay and Sanjay together 8/23 of the work. How much should Ajay be paid?
(a) 245 ₹
(b) 295 ₹
(c) 300 ₹
(d) 345 ₹
Solution: Total work= 23 unit
A+V=19, S=4
V+S=8, A=15
V+4=8
V=4
A:V:S= 15:4:4
Ajay’s income= 529×15/23= 345 ₹
Option (d) is correct.
Que 8: Ashok and Mohan can do a piece of work in 12 days. Mohan and Binod together do it in 15 days. If Ashok is twice as good a workman as Binod. In how much time will Mohan alone be able to do the work?
(a) 15 days
(b) 20 days
(c) 25 days
(d) 35 days
Solution: A+M⇒12 days
M+B⇒15 days
A:B:M=2:1:k
Total work=(2+k)×12= (k+1)×15
k=3
Time taken by Mohan= Total work/3= 60/3= 20 days
Option (b) is correct.
Que 9: 24 men working 8 h a day can finish a work in 10 days. Working at a rate of 10 h a day, the number of men required to finish the 3/4th of the work in 6 days is
(a) 30
(b) 32
(c) 28
(d) 24
Solution: 24×8×10= (k×10×6)÷(3/4)
k= 24
Option (d) is correct.
Que 10: 12 men complete a work in 18 days. 6 days after they had started working, 4 men joined them. How many more days will all of them take to complete the remaining work?
(a) 10 days
(b) 12 days
(c) 15 days
(d) 9 days
Solution: M⇒ 1 unit/day
Total work= 12×18=216 unit
12×6+16×t=216
t=9 days
Option (d) is correct.
Que 11: A takes 5 days more than B to do a certain job and 9 days more than C. A and B together can do the job in the same time as C. How many days A would take to do it?
(a) 16 days
(b) 10 days
(c) 15 days
(d) 20 days
Solution: A⇒t+9
B⇒t+4
C⇒t
A+B=C
1/(t+9) +1/(t+4)=1/t
t=15 (by options)
Option (c) is correct.
Que 12: Abbot can do some work in 10 days, Bill can do it in 20 days and Clinton can do it in 40 days. They start working in turns with Abbot starting to work on the first day followed by Bill on the second day and by Clinton on the third day and again by Abbot on the fourth day and so on till the work is completed fully. Find the time taken to complete the work fully?
(a) 16 days
(b) 15.33 days
(c) 17 days
(d) 16.5 days
Solution: Ratio of Efficiencies⇒ A:B:C= 4:2:1
Total work= 4×10= 40 unit
(3 days⇒7 unit)×5
15 days⇒35 unit ……….(i)
Abbot⇒4 unit in 1 day ………(ii)
Bill⇒1 unit in 0.5 day ……..(iii)
Required days= 15+1+0.5=16.5 days
Option (d) is correct.
Que 13: A, B and C can do some work in 36 days. A and B together do twice as much work as C alone and A and C together can do thrice as much work as B alone. Find the time taken by C to do the whole work.
(a) 72 days
(b) 96 days
(c) 108 days
(d) 120 days
Solution: A+B+C⇒ 36 days
A+B : C=(2:1)×4=8:4
A+C : B=(3:1)×3=9:3
A:B:C= 5:3:4
Total work= 12×36 unit
Time taken by C= (12×36)/4=108 days
Option (c) is correct.
Que 14: A cistern is normally filled in 6 h but takes 4 h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?
(a) 15 h
(b) 16 h
(c) 20 h
(d) None of these
Solution: Inlet A⇒ 6 h
Inlet A+Outlet B⇒ 10 h
Ratio of efficiencies⇒ A: (A+B)=5:3
B⇒ -2 unit/h
Tank capacity=5×6 =30 unit
Time taken by B=30/2 =15 h
Option (a) is correct.
Que 15: Considering the two taps are running continuously to fill a tank, with the 1st tap able to fill the tank in 5 hours and the 2nd tap able to fill it in 20 hours, there was an unfortunate delay of one hour in filling the tank due to an unnoticed leak. Can you determine the time it would take for the leak to empty a fully filled tank?
(a) 15 hours
(b) 20 hours
(c) 25 hours
(d) 40 hours
Solution: Inlet A⇒5 h, B⇒20 h
Ratio of efficiencies⇒ A:B=4:1
Tank capacity=20 unit
A+B⇒4 h
A+B+Outlet C⇒5 h
A:B:C=+4:+1:-1
Time taken by C=20/1= 20 h
Option (b) is correct.
Assignment-2
Que 1: 8 taps are fitted in a tank in which some are inlet taps and some are outlet taps. Each inlet tap can fill the tank in 15 hours and each outlet tap can empty the tank in 30 hours. Find the number of inlet taps if the whole tank is filled in 3 hours when all 8 taps are open.
(a) 5
(b) 7
(c) 6
(d) 4
Solution: Ratio of efficiency of inlet and outlet taps= +2: -1
{2a-1(8-a)}×3=2×15
9a-24=30
a=6
Option (c) is correct.
Directions for Questions 2 to 3: Read the following and answer the questions that follow.
A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.
Que 2: If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?
(a) 16 minutes
(b) 13 minutes
(c) 7 minutes
(d) None of these
Solution: Set X⇒20 min
Set Y⇒16 min
Set Z⇒(-)20 min
Total work= 80 unit
Efficiency=4+5-4=5 unit/min
Required time= 49% of 80÷5= 7.84 min
Option (d) is correct.
Que 3: If one pipe is added for set X and set Y and set Z’s capacity is increased by 20% on its original value and all the taps are opened at 2:58 p.m., then at what time does the tank get filled? (If it is initially empty)
(a) 3:05 pm
(b) 3:04 pm
(c) 3:10 pm
(d) 3:03 pm
Solution: Set X (11 pipes)⇒ 100/11 min
Set Y (6 pipes)⇒ 20/3 min
Set Z (+20%)⇒ (-)50/3 min
Required time= 100/20= 5 min
2:58 pm+5 min=3:03 pm
Option (d) is correct.
Que 4: What is the outlet flow rate in litres per minute if a tank with a capacity of 25 litres has both its inlet and outlet taps opened simultaneously, and the tank gets filled in 5 minutes? Also, when the outlet flow rate is doubled and both taps are opened, the tank never gets filled up.
(a) 2
(b) 6
(c) 4
(d) 3
Solution: Let the flow rates of the inlet and outlet pipes be a and b respectively.
a-b=25/5=5
a-2b≤0
a≤2b
5+b≤2b
5≤b
Option (b) is correct.
Que 5: A, B and C working together completed a job in 10 days. However, C only worked for the first three days when 37/100 of the job was done. Also, the work done by A in 5 days is equal to the work done by B in 4 days. How many days would be required by the slowest worker to complete the entire work?
(a) 20 days
(b) 25 days
(c) 30 days
(d) 40 days
Solution: 5A=4B
A:B=4:5
7(A+B)= 63 unit
A+B=9 unit
A=4 unit & B=5 unit
3(A+B+C)=37
3(9+C)=37
C=10/3
Time taken by C= 100/(10/3)=30 days
Option (c) is correct.
Que 6: It takes six days for three women and two men working together to complete a work. Three men would do the same work five days sooner than nine women. How many times does the output of a man exceed that of a woman?
(a) 3 times
(b) 4 times
(c) 5 times
(d) 6 times
Solution: 3W+2M⇒6 days
3M⇒x-5
9W⇒x
From options: M/W=6
M= 6 unit/day & W=1 unit/day
Total work= (3×1+2×6)×6=90 unit
Days taken by 3 Men to complete the task= 90/18= 5 days
Days taken by 9 Women to complete the task=90/9= 10 days
Option (d) is correct.
Que 7: Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need eight hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design?
(a) 10.5 hours
(b) 12.5 hours
(c) 14.5 hours
(d) 18.5 hours
Solution: R+U⇒t
R⇒t+4.5
U⇒t+8
t=\sqrt{4.5\times 8}=6 hours
R⇒6+4.5=10.5 hours
Option (a) is correct.
Que 8: Mini and Vinay are quizmasters preparing for a quiz. In x minutes, Mini makes y questions more than Vinay. If it were possible to reduce the time needed by each to make a question by two minutes, then in x minutes Mini would make 2y questions more than Vinay. How many questions does Mini make in x minutes?
(a) \frac{1}{4}\left[2(x+y)-\sqrt{2x^2+4y^2}\right].
(b) \frac{1}{4}\left[2(x-y)-\sqrt{2x^2+4y^2}\right].
(c) Either a or b
(d) \frac{1}{4}\left[2(x-y)-\sqrt{2x^2-4y^2}\right].
Solution: Let total time= 24 min
Mini takes 6 minutes to make a question; total questions= 24/6= 4
Vinay takes 8 minutes to make a question; total questions= 24/8= 3
y= 4-3=1……(i)
Mini takes 6-2=4 min to make a question; total questions= 24/4= 6
Vinay takes 8-2=6 min to make a question; total questions= 24/6= 4
Difference=6-4=2 or 2y…… (ii)
For x=24 and y=1, the answer should be 4
Option (a) is correct.
Que 9: Two pipes A and B can fill up a half full tank in 1.2 hours. The tank was initially empty. Pipe B was kept open for half the time required by pipe A to fill the tank by itself. Then, pipe A was kept open for as much time as was required by pipe B to fill up 1/3 of the tank by itself. It was then found that the tank was 5/6 full. The least time in which any of the pipes can fill the tank fully is:
(a) 4.8 hours
(b) 4 hours
(c) 3.6 hours
(d) 6 hours
Solution: Let the tank’s capacity= 12 unit
Efficiency of A+B= 12/(12/5)= 5 unit/hr
A⇒x hr
B⇒y hr
A is kept open for y/3 hours and B is kept open for x/2 hours
5/6th part of the tank= (5/6)×12= 10 unit
From options; if x=4 hr
Efficiency of A= 12/4= 3 unit/hr
Efficiency of B= 5-3= 2 unit/hr; time required to fill the tank (y)= 12/2= 6hr
3×(6/3)+2×(4/2)=10 unit (Condition satisfied)
Option (b) is correct.
Que 10: A tank of 425 litres capacity has been filled with water through two pipes, the first pipe having been opened five hours longer than the second. If the first pipe were open as long as the second, and the second pipe was open as long as the first pipe was open, then the first pipe would deliver half the amount of water delivered by the second pipe; if the two pipes were open simultaneously, the tank would be filled up in 17 hours. How long was the second pipe open?
(a) 10 hours
(b) 12 hours
(c) 15 hours
(d) 18 hours
Solution: A+B⇒17 hr
Efficiency of A+B= a+b= 425/17= 25 litres/hr ……..(i)
Time for which pipe A is open⇒t+5
Time for which pipe B is open⇒t
From options; t=15 hr
a:b=2:3
a=10 litre/hr & b=15 litre/hr………(ii)
a×20 hr+ b×15 hr=200+225=425 (Satisfied)
Option (c) is correct.
Que 11: Two men and a woman are entrusted with a task. The second man needs three hours more to cope with the job than the first man and the woman would need working together. The first man, working alone, would need as much time as the second man and the woman working together. The first man, working alone, would spend eight hours less than the double period of time the second man would spend working alone. How much time would the two men and the woman need to complete the task if they all worked together?
(a) 2 hours
(b) 3 hours
(c) 4 hours
(d) 5 hours
Solution: A⇒y hr; A+W⇒x hr
B⇒x+3 hr; B+W⇒y hr
y=2(x+3)-8
2x-y=2 ……(i)
A=B+W
A+B+W=2A⇒y/2 hr
From options if y/2=2 hr
y=4
2x-y=2 ……(i)
x=3
If A⇒4 hr; A+W⇒3 hr
Then W⇒12 hr
B⇒6 hr
Then A+B+C⇒2 hr (satisfied)
Option (a) is correct.
Directions for question number 12 & 13:
Que 12: In the ancient city of Portheus, the emperor has installed an overhead tank that is filled by two pumps X and Y. X can fill the tank in 12 hours while Y can fill the tank in 15 hours. There is a pipe Z which can empty the tank in 10 hours. Both the pumps are opened simultaneously. The supervisor of the tank before going out on work, asks his assistant to open Z when the tank is exactly 40% filled so that tank is exactly filled up by the time he is back. If he starts X and Y at exactly 11:00 AM and he comes back at A:B. Then find the value of A+ B.
(a) 38
(b) 41
(c) 25
(d) Can not be determined
Solution: X⇒12 hr
Y⇒15 hr
-Z⇒10 hr
Tank capacity= 60 unit
Ratio of efficiencies= 5:4:-6
Time taken to fill 40% of the tank= 24/9=8/3 hr =2 hr 40 min
Time taken to fill rest 60% of the tank= 36/3= 12 hr
Total time= 12+ 2 hr 40 min= 14 hr 40 min
11:00 AM+ 14 hr 40 min= 1:40 AM
A+B=1+40=41
Option (b) is correct.
Que 13: Due to a miscalculation by the assistant, he opens Z when the tank is one fourth filled. If the supervisor comes back as per the plan what percent of the tank is still empty?
(a) 5
(b) 6.66
(c) 10
(d) 12.5
Solution: Time taken to fill 25% of the tank= 15/9=5/3 hr =1 hr 40 min
Time taken to fill rest 75% of the tank= 45/3= 15 hr
Total time= 15+1 hr 40 min= 16 hr 40 min
16 hr 40 min- 14 hr 40 min= 2 hr (before)
Supervisor will find tank 6 litres or 10% (3 litre/hr×2 hr= 6 litre) empty
Option (c) is correct.
Que 14: Three students A, B and C were working on a project. A is 40% more efficient than B, who is 40% more efficient than C. A takes 10 days less than B to complete the project. A starts the project and works for 10 days and then B takes over. B works on the project for the next 14 days and then stops the work, handing it over to C to complete it. In how many days, would C complete the remaining project?
(a) 10
(b) 8
(c) 7.5
(d) 9.8
Solution: Ratio of Efficiencies of A:B:C= 49:35:25
Time taken by A and B to complete the work are ta and tb respectively
ta:tb=Eb:Ea=100:140=5:7
ta=25 days
Total work= 49×25=1225 unit
49×10+35×14+25×k=1225
k=9.8 days
Option (d) is correct.
Que 15: The Bubna dam has four inlets. Through the first three inlets, the dam can be filled in 12 minutes; through the second, the third and the fourth inlet, it can be filled in 15 minutes; and through the first and the fourth inlet, in 20 minutes. How much time will it take all the four inlets to fill up the dam?
(a) 8 min
(b) 10 min
(c) 12 min
(d) None of these
Solution: A+B+C⇒12 min
B+C+D⇒15 min
A+D⇒20 min
Total work= 60 unit
Efficiency of A+B+C=5 unit/min
B+C+D=4 unit/hr
A+D=3 unit/hr
A+2(B+C)+D=9
3+2(B+C)=9
B+C=3 unit/hr
A+B+C+D=2+3+1=6 unit
Required time to fill the dam= 60/6=10 min
Option (b) is correct.
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