Arithmetic sample questions to ace police exam

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 and solutions on the Time and Work topic. Pipes and Cisterns: Nature of Pipe: Inlet: A pipe connected to a tank or reservoir for filling is called as inlet. Outlet: A […]

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 and solutions on the Time and Work topic.

Pipes and Cisterns:
Nature of Pipe:
Inlet: A pipe connected to a tank or reservoir for filling is called as inlet.
Outlet: A pipe connected with a tank and used for emptying it is called outlet.

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Example: A tank can fill with water by a pipe in 5 hours and it can be emptied by a second pipe in 4 hours. If both pipes are opened, find the time needed to empty the tank?
Ans: 20 hours
Given: Time taken by tanks 5h, 4h, take LCM of 5,4 = 20 (see the table)
Follow red arrow
Now, net speed of both tanks will be -1.
To calculate time taken, divide 20/-1 = 20.

Practice questions:

1. If A can do a piece of work in 5 days, B in 10 days and C in 30 days, they can do it together in
A. 3 days B. 4 days C. 5 days D. 6 days
Ans: A
Explanation:
If A can do a piece of work in n days, work done by A in 1 day = 1/n
Work done by A in 1 day = 1/5
Work done by B in 1 day = 1/10
Work done by C in 1 day = 1/30
A+B+C 1 day work = 1/5 + 1/10 + 1/30 = (6+3+1)/30 = 1/3
If P does 1/n work in a day, P can finish the work in n days
Therefore A+B+C can do a piece of work in 3 days.
Shortcut: LCM of Sum of factors = 30 / 6 + 3 + 1 = 30 / 10 = 3 days.

2. A and B can do a piece of work in 6 days and A alone can do it in 9 days. B alone can do it in ____ days
A. 16 B. 18 C. 20 D. 22
Ans: B
Explanation:
Work done by A+B in 1 day = 1/6
Work done by A in 1 day = 1/9
Work done by B in 1 day = (1/6) – (1/9)= 1/18
Therefore, B can do a piece of work in 18 days

3. A and B can do a piece of work in 12 days, B and C in 15 days and C and A in 20 days. They can do it in together in ____ days
A. 30 B. 20 C. 10 D. 5
Ans: C
Explanation:
Work done by A+B in 1 day = 1/12
Work done by B+C in 1 day = 1/15
Work done by C+A in 1 day = 1/20
By adding we get 2(A+B+C) 1 day’s work = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 1/5
(A+B+C) 1 day’s work= (1/5) * (1/12) = 1/10
Therefore, A+B+C can do a piece of work in 10 days

4. A and B can do a piece of work in 15 and 20 days viz. With the help of C, if they can do it in 5 days, then C alone can do it in ____ days
A. 10 B. 11 C. 12 D. 13
Ans: C
Explanation:
Work done by A in 1 day = 1/15
Work done by B in 1 day = 1/20
Work done by A+B in 1 day = (1/15) + (1/20) = (4+3)/60 = 7/60
Work done by A+B+C in 1 day = 1/5
Work done by C in 1 day = (1/5) – (7/60) = 1/12
Therefore, C can do a piece of work in 12 days.

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