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Maths Quiz for KVS and NVS Exams Q1. Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is  full a leak develops in the tank through which  of the water supplied by both the pipes out. What is the total time taken to fill the tank?
(a) 16 hr
(b) 8 hr
(c) 12 hr
(d) 14 hr

Q2. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively both the pipes are opened together. But, after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
(a) 10 min 20 sec
(b) 11 min 45 sec
(c) 12 min 30 sec
(d) 14 min 40 sec

Q3. Two pipes can fill a cistern in 14 hrs and 16 hrs respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it?
(a) 96 hours
(b) 102 hours
(c) 106 hours
(d) 112 hours

Q4. A cistern has three pipes A, B and C. A and B can fill it in 3 hrs and 4 hrs respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3 P.M., 4 P.M. and 5 P.M. respectively, at what time will the cistern be empty?
(a) 6 : 15 P.M.
(b) 7 : 12 P.M.
(c) 8 : 12 P.M.
(d) 8 : 35 P.M.

Q5. Pipes A and B can fill a tank in 5 and 6 h, respectively. Piece C can fill it in 30 h. If all the three pipes are opened together, then in how much time the tank will be filled up?
(a) 3 3/14  h
(b) 2 1/2 h
(c) 3 9/14 h
(d) 2 1/14 h

Q6. A and B together can complete a work in 3 days. They start together. But, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in
(a) 10 days
(b) 4 days
(c) 6 days
(d) 8 days

Q7. In a 4 km race A wins by 600 m over B. B can give start of 200 m to C in a 4 km race. By how much distance C gets start up so that the race between A and C ends in dead heat in the same race of 4 km?
(a) 770m
(b) 670m
(c) 530m
(d) 830m

Q8. A man can row at 5 km/hr in still water. If the river is running at 1 km/hr it takes him 75 minutes to row to a place and back. How far is the place?
(a) 2.5 km
(b) 3 km
(c) 4 km
(d) 5 km

Q9. Two trains of length 105 m and 90 m, respectively run at the speeds of 45 km/h and 72 km/h, respectively in opposite directions on parallel tracks. Find the time which they take to cross each other.
(a) 5s
(b) 6s
(c) 7s
(d) 8s

Q10. Two trains A and B start running together from the same point in the same direction at 60 kmph and 72 kmph respectively. If the length of each train is 240 m, how long will it take for the train B to cross train A?
(a) 1 min 12 sec
(b) 1 min 24 sec
(c) 2 min 12 sec
(d) 2 min 24 sec
Solutions

S1. Ans.(a)
Sol. Time taken by the two pipes to fill the tank =(20 × 30)/(20 + 30) = 12 hrs.
1/3 of tank is filled in 12/3 = 4 hours.
Now, 1/3 of the supplied water leaks out
The filler pipes are only 1-(1/3)=2/3 as efficient as earlier.
The work of (12-4=8) hour will complete now in
8×3/2=12
Total time =12+4=16 hr

S2. Ans.(d)
Sol. Part filled by both in 4 min
=4×(1/15 + 1/20)=(4×7/60)=7/15
unfilled =(1-(7/15))=8/15
1/20 part is filled by B in 1 min
8/15 part is filled B in =(20×8/15) min
=32/3 min = 10 min 40 sec
Total time taken = (4 min + 10 min 40 sec)
= 14 min 40 sec

S3. Ans.(d)
Sol. Work done by two pipes in 1 hr
=(1/14 + 1/16)=15/112
Total time taken by two pipes and leak in 1 hr
=(112/15 + 32/60) = 8 hrs
Work done by the leak in 1 hr
=(15/112 – 1/8)=1/112
Hence, the leak will empty the full cistern in 112 hrs.

S4. Ans.(b)
Sol. Let the cistern be emptied in x hours after 3 P.M.
Work done by A in x hrs by B in (x – 1) hrs and by C in (x – 2) hrs = 0
⇒ (x/3)+(x – 1)/4-(x-2)
⇒ 4x + 3(x – 1) – 12(x – 2) = 0
⇒ 5x = 21 ⇒ x = 4 hrs 12 min.
Required time is 7 : 12 P.M.

S5. Ans.(b)
Sol.
Net part filled in 1 h =(1/5+1/6+1/30)
=(6 + 5 + 1)/30=12/30=2/5
∴ Required time =5/2= 2 1/2h

S6. Ans.(c)
Sol. (A + B)’s 2 day’s work =2/3
Remaining work =1-(2/3)=2/3
Time taken by A in doing =1/3
Work = 2 days
∴ Time taken by A in completing the work = 6 days
∴ B’s 1 day’s work =(1/3)-(1/6)=(2 – 1)/6=1/6
∴ B alone will completely the work in 6 days.

S7. Ans.(a)
Sol. Ratio of speeds of A : B = 4000 : 3400 = 20 : 17
Ratio of speeds of B : C = 4000 : 3800 = 20 : 19
Ratio of speeds of A : B : C = 400 : 340 : 323
Therefore, in 4000 m race A run 4000 m,
B run 3400 m and C run 3230 m. thus C can get 770 m start up from A.

S8. Ans.(b)
Sol. Speed downstream = (5 + 1) = 6 km/hr
Speed upstream = (5 – 1) = 4 km/hr
Let the required distance be x km
Then, (x/6)+(x/4)=75/60=5/4
⇒ (2x + 3x) = 15
⇒ 5x = 15
⇒ x = 3
Required distance = 3km

S9. Ans.(b)
Sol. Total length of the train = (105 + 90) = 195m
Relative speed = (72 + 45) = 117 km/h
=(117×5/18)=585/18 m/s
∴ Required time =(195×18/585)s=6s

S10. Ans.(d)
Sol. Relative speed = (72 – 60) kmph = 12 kmph
=(12×5/18)=10/3 m/sec
Total distance covered = (240 + 240) = 480m
Required time =(480×3/10) = 144 sec
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