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Question 1 of 5
1. Question
A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?
Correct
Solution: D
As per the given information, the velocity of the stream is 4 km/hr.
The speed of the boat in still water is 10 km/hr.
Therefore, speed of boat in downstream = (10+4) = 14 km/hr.
The speed of boat in upstream = (10-4) = 6 km/hr.
Let the distance between A and B be ‘x’. As C is in the midway between A and B, distance between B and C is x/2.
Total time taken to reach is 26 hours.
Therefore, x/14 + (x/2)/6 = 26
- x/14 + x/12 = 26
- (7x+6x)/84 = 26
- 13 x /84 = 26
- x/84 = 2
- x = 168.
The distance between A and B is 168 km.
Hence, option (d) is correct.
Incorrect
Solution: D
As per the given information, the velocity of the stream is 4 km/hr.
The speed of the boat in still water is 10 km/hr.
Therefore, speed of boat in downstream = (10+4) = 14 km/hr.
The speed of boat in upstream = (10-4) = 6 km/hr.
Let the distance between A and B be ‘x’. As C is in the midway between A and B, distance between B and C is x/2.
Total time taken to reach is 26 hours.
Therefore, x/14 + (x/2)/6 = 26
- x/14 + x/12 = 26
- (7x+6x)/84 = 26
- 13 x /84 = 26
- x/84 = 2
- x = 168.
The distance between A and B is 168 km.
Hence, option (d) is correct.
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Question 2 of 5
2. Question
Four persons are chosen at random from a group of 3 men, 5 women and 4 children. What is the probability of exactly two of them being men?
Correct
Solution: B
Total sample size of selecting 4 people out of 12 people (3 men, 5 women and 4 children) = 12c4= 495.
Various possibilities of having exactly two men in the group of four are:
(2 men AND 2 women) OR (2 men AND 2 children) OR (2 men AND 1 woman and 1 child)
Thus, it can be written in formula: (3c2 * 5c2) + (3c2 * 4c2) + (3c2 *5c1 *4c1)
è (3*10) + (3 * 6) + (3 *5*4) = 30+18+60 = 108.
Therefore, probability of exactly two of them being men is 108/495 = 12/55
Hence, option (b) is correct.
Incorrect
Solution: B
Total sample size of selecting 4 people out of 12 people (3 men, 5 women and 4 children) = 12c4= 495.
Various possibilities of having exactly two men in the group of four are:
(2 men AND 2 women) OR (2 men AND 2 children) OR (2 men AND 1 woman and 1 child)
Thus, it can be written in formula: (3c2 * 5c2) + (3c2 * 4c2) + (3c2 *5c1 *4c1)
è (3*10) + (3 * 6) + (3 *5*4) = 30+18+60 = 108.
Therefore, probability of exactly two of them being men is 108/495 = 12/55
Hence, option (b) is correct.
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Question 3 of 5
3. Question
A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
Correct
Solution: C
From the given data, we can get
A’s one day work = 1/24,
B’s one day work = 1/9 and
Cs one day work = 1/12.
Since, B and C start the work and left after 3 days, the work done by B and C is 3 *((1/9) +(1/12)) = 7/12.
Therefore, remaining work = 1- 7/12 =5/12.
Time taken by A to complete the remaining work = 24 * 5/12 =10 days.
Hence, option (c) is correct.
Incorrect
Solution: C
From the given data, we can get
A’s one day work = 1/24,
B’s one day work = 1/9 and
Cs one day work = 1/12.
Since, B and C start the work and left after 3 days, the work done by B and C is 3 *((1/9) +(1/12)) = 7/12.
Therefore, remaining work = 1- 7/12 =5/12.
Time taken by A to complete the remaining work = 24 * 5/12 =10 days.
Hence, option (c) is correct.
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Question 4 of 5
4. Question
How many words of 4 letters with or without meaning be made from the letters of the word ‘NUMBER’, when repetition of letters is not allowed?
Correct
Solution: D
To form the word we use arrangement.
The word NUMBER have 6 alphabets.
Therefore, to form 4 letter word from the word NUMBER is 6P4= 6!/2!
- 6*5*4*3* 2!/2!
- 360
Hence, option (d) is correct.
Incorrect
Solution: D
To form the word we use arrangement.
The word NUMBER have 6 alphabets.
Therefore, to form 4 letter word from the word NUMBER is 6P4= 6!/2!
- 6*5*4*3* 2!/2!
- 360
Hence, option (d) is correct.
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Question 5 of 5
5. Question
Tina goes to school from her house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If she takes 5 hours in total, then what is the distance between her house and school?
Correct
Solution: A
Let the distance between Tina’s house and school be ‘x’ km.
Therefore, time to cover the distance from her house to school =
(Distance/ speed) = (x/3) hours.
Similarly, time to cover the distance from her school to house = (x/2) hours.
It is given that total time taken for whole journey= 5 hours.
Thus, (x/3 + x/2)= 5
- ((2x+3x)/6)= 5
- (5x/6)=5
- 5x=30 or x=6
Thus, distance between her house and school is 6 km.
Hence, option (a) is correct
Incorrect
Solution: A
Let the distance between Tina’s house and school be ‘x’ km.
Therefore, time to cover the distance from her house to school =
(Distance/ speed) = (x/3) hours.
Similarly, time to cover the distance from her school to house = (x/2) hours.
It is given that total time taken for whole journey= 5 hours.
Thus, (x/3 + x/2)= 5
- ((2x+3x)/6)= 5
- (5x/6)=5
- 5x=30 or x=6
Thus, distance between her house and school is 6 km.
Hence, option (a) is correct
