Nail the arithmetic questions in SI exam

By Banda Ravipal Reddy

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions, answers and explanations on the Pipes and Cisterns topic.

1. One filling pipe A is 5 times faster than second filling pipe B. If B can fill a cistern in 36 minutes, the find the time when the cistern will be full if both fill pipes are opened together.
a) 6 minutes b) 8 minutes c) 4 minutes d) 12 minutes
Ans: a

Explanation:

Pipe B can fill a cistern in 36 minutes,
=>; Pipe B can fill in 1 min = 1/36
Pipe A is 5 times faster than pipe B.

=>; Pipe A can fill in 1 min = 5/36

Pipe A and B together fill in 1 min = 1/36 5/36
= 6/36 = 1/6

Hence, tank will be filled in 6 minutes.
2. If the ratio of rate of filling of two Pipes A and B is 3:2. If together they can fill a tank 5/6th of tank in 20 minutes. Then in how many does A alone can fill the Tank?
a) 20 Minutes b) 30 Minutes c) 40 Minutes d) 50 Minutes

Ans: c
Explanation:

5/6 tank = 20 Min
Full tank = 24 Min
Time taken to fill the tank is reciprocal to the rate of filling

Time taken by A and B will be 2:3

1/2x 1/3x = 1/24

x = 20, A= 2x = 40 minutes.

Previous year questions

3. A pipe of diameter ‘d’ can drain a water tank in 40 minutes. The time taken by a pipe of diameter ‘2d’ for doing the same job is (in minutes)

a) 5 b) 10 c) 20 d) 50

Ans: b

Explanation:

Pipe 1: Pipe 2

Diameter D: 2D

area π( D/2)2 : π (2D/2)^2 = Πd2: 4Πd2
efficiency of draining 1 : 4

Pipe 1 : Pipe 2 = efficiency 1 : 4
***BOX***

4. A pump can fill a tank with water in 2 hours. Because of leakage it took 2 1/3 hours to fill the tank. The time taken to empty the full tank due to leakage (in hours) is
a) 8 b)7 c) 10 d) 14

Ans: d

Explanation:
The rate of filling the tank by pipe = 1/2

Again with the leakage the pipe takes 2 1/3 hours i.e. 7/3 hours

The rate of filling the tank by pipe along with the leakage will be 3/7

The rate of leak in the tank is ( 1/2 – 3/7 ) = 1/14

The time taken by the leak to empty the tank = 1/(1⁄14) = 14 hours.
5. A water tank is 2/5th full. Pipe A can fill the tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, the time to empty or fill the tank completely is

a) 6 minutes to empty b) 6 minutes to fill

c) 9 minutes to empty d) 9 minutes to fill

Ans: a

Explanation:
Since pipe B is faster, the tank will be emptied.

Work done by pipe A in 1 min = 1/10

Work done by pipe B in 1 min = 1/6
Total work when A and B are opened = 1/6 – 1/10 = 4/60 = 1/15

Part emptied in by A and B in 1 min = 1/15
Time taken to empty 2/5 of the tank = (2/5)/ (1/15) = 6 min

6. Taps A and B fill can empty tank individually in 8 hours and 6 hours respectively, while tap C empties the full tank in 12 hours. Due to a problem tap C could not be closed. If the taps A and B are opened alternately for one hour each starting with A, the time taken (in hours) to fill the tank is:

a) 6 b) 8 c) 16 d) 24
Ans: c

Explanation:

Tap A can fill in 8 hr. B in 6 hr., C can empty reservoir in 12 hr.
Part filled by all 3 can fill tank in 1 hrs. = 1/8 1/6 -1/12 = 5/24

Due to a problem tap C could not be closed, if the taps A and B are opened alternately for one hour each starting with A.
For the first hour (A C) works together

For the second hour (B C) works together

(A C)’s 1 hour work = 1/8 – 1/12 = 1/24

(B C)’s 1 hour work = 1/6 – 1/12 = 2/24
Total work units = 24

3 units work =>; 2 hours

24 units work =>; 16 hours.

Director, SIGMA
Sai Institute of General Mental Ability
Hyderabad

 

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