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Question 1 of 5
1. Question
A man travels a distance of 12 km at 3 km/hr, another distance of 12km at 4 km/hr and a third distance of 12km at 6 km/hr. His average speed for the whole journey is:
Correct
Solution: C
The Average speed= (Total Distance/Total Time taken)
Time taken to cover first 12 km= (Distance/Speed)= (12/3)= 4 hours
Time taken to cover second 12 km= 12/4= 3 hours
Time taken to cover last 12 km= 12/ 6= 2 hours
Hence, total time taken for whole journey= (4+3+2) hours= 9 hours
Therefore, the average speed of whole journey= (Total distance/total time)
- Average speed of man= (36/9)= 4 km/hr
- Hence, option (c) is correct.
Incorrect
Solution: C
The Average speed= (Total Distance/Total Time taken)
Time taken to cover first 12 km= (Distance/Speed)= (12/3)= 4 hours
Time taken to cover second 12 km= 12/4= 3 hours
Time taken to cover last 12 km= 12/ 6= 2 hours
Hence, total time taken for whole journey= (4+3+2) hours= 9 hours
Therefore, the average speed of whole journey= (Total distance/total time)
- Average speed of man= (36/9)= 4 km/hr
- Hence, option (c) is correct.
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Question 2 of 5
2. Question
If two fair dices are thrown simultaneously, what is the probability of getting a total score of 6?
Correct
Solution: C
Total possible values obtained after throwing first dice = 6.
Total possible values obtained after throwing second dice = 6.
Therefore, total possible values after throwing two fair dices simultaneously is (6X6) = 36.
Various possibilities of getting sum of 6 is (1,5), (2,4), (3,3),(4,2) and (5,1) = 5.
Thus, probability of getting the sum of 6 = 5/36.
Hence, option (c) is correct.
Incorrect
Solution: C
Total possible values obtained after throwing first dice = 6.
Total possible values obtained after throwing second dice = 6.
Therefore, total possible values after throwing two fair dices simultaneously is (6X6) = 36.
Various possibilities of getting sum of 6 is (1,5), (2,4), (3,3),(4,2) and (5,1) = 5.
Thus, probability of getting the sum of 6 = 5/36.
Hence, option (c) is correct.
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Question 3 of 5
3. Question
In how many different ways can the letter of the word ELEPHANT be arranged so that vowels always occur together?
Correct
Solution: A
When question is about arrangement it is permutation.
Total number of letters in the word ELEPHANT = 8
The vowels in the word ELEPHANT are two Es and one A.
Let’s group all the vowels into a group i.e (EEA) and consider it as single letter.
Now total number of letters will be 5 consonants (L, P, H, N, T) + (EEA) = 6.
Therefore, total arrangement possible = 6! .
However, EEA can be further arranged into (3!)/(2!) (as there are two Es).
Thus, total possible ways that the word ELEPHANT be arranged so that vowels always occur together = 6! * 3!/2!= 6! * 3
- 720 * 3 = 2160 ways.
Hence, option (a) is correct.
Incorrect
Solution: A
When question is about arrangement it is permutation.
Total number of letters in the word ELEPHANT = 8
The vowels in the word ELEPHANT are two Es and one A.
Let’s group all the vowels into a group i.e (EEA) and consider it as single letter.
Now total number of letters will be 5 consonants (L, P, H, N, T) + (EEA) = 6.
Therefore, total arrangement possible = 6! .
However, EEA can be further arranged into (3!)/(2!) (as there are two Es).
Thus, total possible ways that the word ELEPHANT be arranged so that vowels always occur together = 6! * 3!/2!= 6! * 3
- 720 * 3 = 2160 ways.
Hence, option (a) is correct.
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Question 4 of 5
4. Question
A group of men could do a piece of work in 18 days. However, 6 men left the group before the work began and the remaining men in the group completed the work in 20days. What was the original size of the group?
Correct
Solution: A
If M1 persons can do a piece of work in D1 days and M2 persons can do same piece of work in D2 days, then M1*D1= M2 * D2.
Let the original number of men in the group be ‘x’. (M1)
After 6 men left, the size of group be (x-6) men. (M2)
Now using the above formula, we get
x * 18 = (x-6) * 20
- 18x = 20x -120
- 120= 20x-18x
- 120 = 2x
- x=60
Therefore original number of men in the group are 60 men.
Hence, option (a) is correct.
Incorrect
Solution: A
If M1 persons can do a piece of work in D1 days and M2 persons can do same piece of work in D2 days, then M1*D1= M2 * D2.
Let the original number of men in the group be ‘x’. (M1)
After 6 men left, the size of group be (x-6) men. (M2)
Now using the above formula, we get
x * 18 = (x-6) * 20
- 18x = 20x -120
- 120= 20x-18x
- 120 = 2x
- x=60
Therefore original number of men in the group are 60 men.
Hence, option (a) is correct.
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Question 5 of 5
5. Question
A boat sails 6 km/hr in still water, however it takes thrice as much time in going the same at distance against the current when compared to the direction of the current. Find the speed of the current?
Correct
Solution: A
Given condition:
- Speed of the boat in still water = 6 km/hr.
- Speed of boat in downstream = 3 * speed of boat in upstream.
Let the speed of the current be ‘x’ km/hr.
Therefore, speed of the boat in upstream (i.e against the current) = (6-x) km/hr.
Speed of the boat in downstream (i.e in the direction of current) = (6+x) km/hr
Now, substituting values in given condition, we get
- (6+x) = 3 * (6-x)
- 6+x = 18-3x
- 4x=12
- x=3 km/hr
Thus, speed of the current = 3 km/hr.
Hence, option (a) is correct.
Incorrect
Solution: A
Given condition:
- Speed of the boat in still water = 6 km/hr.
- Speed of boat in downstream = 3 * speed of boat in upstream.
Let the speed of the current be ‘x’ km/hr.
Therefore, speed of the boat in upstream (i.e against the current) = (6-x) km/hr.
Speed of the boat in downstream (i.e in the direction of current) = (6+x) km/hr
Now, substituting values in given condition, we get
- (6+x) = 3 * (6-x)
- 6+x = 18-3x
- 4x=12
- x=3 km/hr
Thus, speed of the current = 3 km/hr.
Hence, option (a) is correct.
