வெல்லுங்கள் CSAT 2025 - 13: Q and A - Problems on pipes & races

Questions & Answers (Multiple Choice) - Problems on pipes & races

கொள்குறி வினா- விடைகள் - குழாய் & ஓட்டப்பந்தயம் கணக்குகள்

1. Three pumps working 6 hours a day can fill a tank in two days. Four similar pumps working, in how many hours to work to fill the tank in one day?
a. 6 b. 7
c. 8 d. 9

2. Pipes A and B can fill a tank in 4 hours and 8 hours respectively. Pipe C can empty it in 6 hours. If all the three pipes are opened simultaneously, then the empty tank will be filled in
a. 6 hrs b. 5 hrs
c. 4.8 hrs d. 5.2 hrs

3. A pump can fill an empty tank with water in 3 hours. Because of leak it took 3hours 15 minutes to fill the tank. The leak can drain all the water of the full tank in
a. 16 hrs b. 39hrs
c. 48 hrs d. 52 hrs

4. Two pipes A and B can fill a tank in 30 and 40 minutess respectively. If these two pipes are opened with an outlet pipe, then the tank filled in 24 minutes, then in how many minutes the outlet pipe can empty the full tank?
a. 60 mts b. 46 mts
c. 58 mts d. 50 mts

5. The rates of filling pipes A and B are
20 litres/min. and 33 litres/min. respectively. How long will they take to fill the tank of capacity 2226 litres if both opened simultaneously?
a. 40 mts b. 46 mts
c. 42 mts d. 50 mts

6. Three taps A, B and C can fill a tank in 16 hours, 8 hours and 12 hours respectively. If A is open all the time and B and C open for one hour each alternatively, then the tank will be filled in
a. 8 hrs b. 6hrs
c. 4 hrs d. 10 hrs

7. Three pipes P, Q and R can fill a tank in 12 hours. After working at it together for 4 hours, R is closed and P and Q can fill the remaining part in 14 hours. The number of hours taken by R alone to fill the tank is
a. 18 hrs b. 22 hrs
c. 24 hrs d. 28 hrs

8. A tank has three pipes A, B and C which can fill the tank in 5hrs, 7.5hrs and 6hrs respectively. If the pipes are opened in order 12noon, 12.30p.m and 1.00p.m respectively, when will the tank be full?
a. 2-28p.m b. 2-00p.m
c. 2-30p.m d. 2-40p.m

9. In a game, A can give B 20 points and A can give C 32 points whereas in the same game, B can give C 15 points. How many points make the game.
a. 200 b. 150
c. 100 d. 250

10. A can give B 15 points in a game of 60 and A can give C 25 points in a game of 75. How many points can B give C in a game of 90?
a. 20 b. 10
c. 15 d. 25

11. In a 200m race, A can give B 20m and C 29m. In the same race how many metres B can give C?
a. 25 b. 30
c. 18 d. 10

12. A runs at 5kmph in a 200m race where A gives B a start of 16m and still beats B by 16 seconds. Find the speed of B in kmph.
a. 4.14kmph b. 4 kmph
c. 4.4kmph d. 5 kmph

13. In 200m race, A covers the distance in 54 seconds and B in 72 seconds. In this race, A beats B by (in metres)
a. 25 b. 50
c. 18 d. 60

14. In a 100 metre race A beats B by 17.5m or 3.5 seconds. A's time over the course is
a. 20 sec b. 25 sec
c. 16.5sec d. 28 sec

15. P runs 1.6 times as fast as Q. If P gives Q a start of of 90m, how far must the winning post be so that P and Q might reach at the same time?
a. 200m b. 300 m
c. 260m d. 240 m

Answers

1. d 2. c 3. b 4. a 5. c

6. b 7. d 8. a 9. c 10. b

11. d 12. a 13. b 14. c 15. d

Explanation to Answers

1. Total pump hours needed to fill the tank
= 3×6×2
Required number of hours
= (3×6×2)/(4×1) = 9 hours.

2. The part of the tank filled in one hour
= (1/4) + (1/8) - (1/6) = 5/24.
The empty tank can be filled in
(24/5) hours = 4.8 hrs.

3. The part of the tank by leak in
one hour = (1/3) - (4/13) = 1/39
So the leak will empty the tank
in 39 hours.

4. Let the outlet pipe can empty the full tank in ' t ' minutes.
So the part of the tank filled in one minute if all the three pipes opened simultaneously is
(1/30) + (1/40) - (1/t) = 1/24
-> (1/t) = (1/30) + (1/40) - (1/24)
-> (1/t) = (4+3-5)/(120) = 1/60
-> t = 60
The outlet pipe can empty the full tank in 60 minutes.

5. If both opened simultaneously, the amount of water filled in one minute
= (20 + 33) litres.
Time taken to fill the tank of capacity 2226 litres = (2226)/(53) = 42 minutes.

6. First hour fill up by A and B
= 1/16 + 1/8 = 3/16
Second hour fill up by A and C is
= 1/16 + 1/12 = 7/48
Part of the tank filled in first 2 hours
= 3/16 + 7/48 = 16/48 = 1/3
To fill the tank the time taken
= (2)/(1/3) = 6 hours.

7. Part of the rank filled in 4 hours
= 4/12 = 1/3.
Remaining part = 1 - 1/3 = 2/3
14 hours work of P and Q = 2/3
1 hour work of P and Q = 2/42 = 1/21
R's one hour work = 1/12 - 1/21
= (7-4)/(84) = 1/28
So R alone can fill the tank in 28 hours.

8. The part of the tank filled at 1.00p.m
= 1/5 +(1/2) (2/15) = 4/15.
If all the pipes opened the part of the tank filled = 1/5 + 2/15 + 1/6 = 1/2.
At 1.00p.m, the remaining part to be filled = 1 - 4/15 = 11/15
To fill 4/15, the time taken
(11/15)/(1/2) = 22/15 hrs
= 1 hr 28mts.
So at 2-28 p.m the tank will be filled.

9. Let the points be 'p'
A B C
Points p p - 20 p - 32
p p - 15

Here (p-20)/p = (p - 32)/(p- 15)
->p^2 - 35p + 300 = p^2 - 32p
-> 3p = 300 -> p = 100

10. A can give C 25 points in a game of 75 means (25/75)×60 = 20.
So A can give C 20 points in a game of 60 whereas A can give B 15 points.
In a game of (60-15), B can give C
(20 - 15)points.
i.e., In a game of 45 points B can give C 5 points.
Hence in a game of 90 points B can give C (5/45)×90 = 10 points.

11. Here A : B = 200 : 180
and A : C = 200 : 171
-> when B runs 180 m, C runs only 171m
-> In 180m race B can give C
(180-171)= 9m.
When B runs 200m race, B can give C
(9/180)×200 = 10m
So When B runs 200m race, B can give C
10m

12. Time taken by A to cover 200m
= (200)/{5×(5/18)} = 144sec.
Time taken by B to cover 184m
= 144 + 16 = 160sec
B's speed (184/160)×(18/5)
= 4.14kmph

13. The distance covered by B in
(72 - 54) = 18 seconds is to be calculated.
(200/72) ×18 = 50 m.

14. The distance run by B in 3.5 seconds is 17.5m. Time taken by B to complete the race is
{(3.5)/(17.5)} × 100 = 20 sec.
A's time over the course is
= 20 - 3.5= 16.5 seconds.

15. Ratio of speeds of P and Q is
1.6 : 1 = 8 : 5
So in a 8m race, P gains 3m over Q.
90m will be gained by P in a race of
(8/3) × 90 = 240m.
Hence the winning post is 240m away from the starting point.

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