Aptitude

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

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Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

[A].

1
2

[B].

2
5

[C].

8
15

[D].

9
20

Answer: Option D

Explanation:

Here, S = {1, 2, 3, 4, …., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) = n(E) = 9 .
n(S) 20

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

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Question:
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

[A].

1
2

[B].

3
4

[C].

3
8

[D].

5
16

Answer: Option B

Explanation:

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
     (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
     (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(E) = 27.

P(E) = n(E) = 27 = 3 .
n(S) 36 4

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

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Question:
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

[A].

10

[B].

12

[C].

14

[D].

16

Answer: Option C

Explanation:

Part filled in 2 hours = 2 = 1
6 3
Remaining part = 1 – 1 = 2 .
3 3
(A + B)’s 7 hour’s work = 2
3
(A + B)’s 1 hour’s work = 2
21

C’s 1 hour’s work = { (A + B + C)’s 1 hour’s work } – { (A + B)’s 1 hour’s work }

   = 1 – 2 = 1
6 21 14

C alone can fill the tank in 14 hours.

Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

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Question:
Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

[A].

5 min.

[B].

9 min.

[C].

10 min.

[D].

15 min.

Answer: Option B

Explanation:

Let B be turned off after x minutes. Then,

Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.

x 2 + 1 + (30 – x). 2 = 1
75 45 75
11x + (60 -2x) = 1
225 75

11x + 180 – 6x = 225.

x = 9.

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

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Question:
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

[A].

60 gallons

[B].

100 gallons

[C].

120 gallons

[D].

180 gallons

Answer: Option C

Explanation:

Work done by the waste pipe in 1 minute = 1 – 1 + 1
15 20 24
    = 1 – 11
15 120
    = –  1 .    [-ve sign means emptying]
40
Volume of 1 part = 3 gallons.
40

Volume of whole = (3 x 40) gallons = 120 gallons.

Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:

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Question:
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:

[A].

6 hours

[B].

6 2 hours
3

[C].

7 hours

[D].

7 1 hours
2

Answer: Option C

Explanation:

(A + B)’s 1 hour’s work = 1 + 1 = 9 = 3 .
12 15 60 20
(A + C)’s hour’s work = 1 + 1 = 8 = 2 .
12 20 60 15
Part filled in 2 hrs = 3 + 2 = 17 .
20 15 60
Part filled in 6 hrs = 3 x 17 = 17 .
60 20
Remaining part = 1 – 17 = 3 .
20 20
Now, it is the turn of A and B and 3 part is filled by A and B in 1 hour.
20

Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.

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?

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Question:
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.

Answer: Option D

Explanation:

Part filled in 4 minutes = 4 1 + 1 = 7 .
15 20 15
Remaining part = 1 – 7 = 8 .
15 15
Part filled by B in 1 minute = 1
20
1 : 8 :: 1 : x
20 15
x = 8 x 1 x 20 = 10 2 min = 10 min. 40 sec.
15 3

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.