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Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.
We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
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Question 1 of 5
1. Question
If a person cycled at 10 km/hr to the office from his house, he reaches 6 minutes late. He reached 6 minutes early when he increased his speed by 2 km/hr. What is the distance between his house and office?
Correct
Solution: D
Let the distance between house and office be ‘x’ km.
- Therefore, time taken by the person to reach office if he travels at the speed of 10 km/hr = (x/10) hours
- Time taken by the person to reach office if he travels at the speed of
12 km/hr = (x/12) hours
Thus, time difference = (x/10)-(x/12) = (6x-5x)/ 60 or x/60 — (Eq 1)
Let the actual time the person is supposed to take to reach office be ‘t’ hours.
- Time taken by the person to reach office if he travels at the speed of
10 km/hr = t+6 min or t+(6/60) hour = ((60t+6)/60) hours
- Time taken by the person to reach office if he travels at the speed of
12 km/hr = t-6 min or t-(6/60) = ((60t-6)/60) hours.
Thus, time difference= (60t+6-60t+6)/60 = 12/60 hours … (Eq 2)
Equating the equation 1 and equation 2 we get x/60= 12/60
- x=12km
Therefore, distance between the house of the person and his house is 12kms.
Hence, option (d) is correct.
Incorrect
Solution: D
Let the distance between house and office be ‘x’ km.
- Therefore, time taken by the person to reach office if he travels at the speed of 10 km/hr = (x/10) hours
- Time taken by the person to reach office if he travels at the speed of
12 km/hr = (x/12) hours
Thus, time difference = (x/10)-(x/12) = (6x-5x)/ 60 or x/60 — (Eq 1)
Let the actual time the person is supposed to take to reach office be ‘t’ hours.
- Time taken by the person to reach office if he travels at the speed of
10 km/hr = t+6 min or t+(6/60) hour = ((60t+6)/60) hours
- Time taken by the person to reach office if he travels at the speed of
12 km/hr = t-6 min or t-(6/60) = ((60t-6)/60) hours.
Thus, time difference= (60t+6-60t+6)/60 = 12/60 hours … (Eq 2)
Equating the equation 1 and equation 2 we get x/60= 12/60
- x=12km
Therefore, distance between the house of the person and his house is 12kms.
Hence, option (d) is correct.
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Question 2 of 5
2. Question
There are 5 men and 5 women. In how many ways they can be seated along a circular table, so that men and women are seated in alternative positions?
Correct
Solution: B
When question is about arrangement it is permutation.
‘n’ people can be seated in circular arrangement in (n-1)! ways.
Now 5 men can be seated in circular arrangement in (5-1)! Ways = 4! Ways.
Since, men already seated, to be seated in alternate position we will have 5 places available. Thus, 5 women can be seated in 5! Ways.
Therefore, total number ways such that 5 men and 5 women seated in circular seat in alternate position will be 4! * 5! = 24 * 120 = 2880 ways.
Hence, option (b) is correct.
Incorrect
Solution: B
When question is about arrangement it is permutation.
‘n’ people can be seated in circular arrangement in (n-1)! ways.
Now 5 men can be seated in circular arrangement in (5-1)! Ways = 4! Ways.
Since, men already seated, to be seated in alternate position we will have 5 places available. Thus, 5 women can be seated in 5! Ways.
Therefore, total number ways such that 5 men and 5 women seated in circular seat in alternate position will be 4! * 5! = 24 * 120 = 2880 ways.
Hence, option (b) is correct.
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Question 3 of 5
3. Question
Aman can complete a piece of work in 5 days, but with the help of his son he can finish the same piece of work in 3 days. Find the time taken by the son alone to complete the work?
Correct
Solution: D
If A can do a work in ‘x’ days and A + B can do the same work in ‘y’ days, then the number of days required to complete the work if B works alone is given by the formula: ( x * y)/(x-y).
Aman alone takes 5 days (i.e x) to complete a piece of work and along with his son he can complete same of piece of work in 3 days(i.e y).
Therefore, his son alone takes ( x * y)/(x-y) days to complete the same piece of work. By substituting the given values in formula, his so will take
- (5 * 3)/(5-3)
- 15/2
- 5 days.
Hence, option (d) is correct.
Incorrect
Solution: D
If A can do a work in ‘x’ days and A + B can do the same work in ‘y’ days, then the number of days required to complete the work if B works alone is given by the formula: ( x * y)/(x-y).
Aman alone takes 5 days (i.e x) to complete a piece of work and along with his son he can complete same of piece of work in 3 days(i.e y).
Therefore, his son alone takes ( x * y)/(x-y) days to complete the same piece of work. By substituting the given values in formula, his so will take
- (5 * 3)/(5-3)
- 15/2
- 5 days.
Hence, option (d) is correct.
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Question 4 of 5
4. Question
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is opened all the time and B and C are opened one hour each alternatively , the tank will be full in :
Correct
Solution: D
Tank filled in one hour when the taps A and B are open = (1/12)+(1/15)= 9/60= 3/20.
Tank filled in one hour when the taps A and C are open = (1/12) + (1/20) = 8/60 = 2/15
Therefore, part of the tank filled in two hours = (3/20) + (2/15) = 17/60.
Part filled in 6 hours = ( 17/60) * 3 = 51/60
Remaining part = 9/60 = 3/20After 6 hours Now it is (A+B)’s turn
Time taken by the A+B to fill 3/20 part = 1 hour
Therefore, total time taken = 6+1 = 7 hoursHence, option (d) is correct.
Incorrect
Solution: D
Tank filled in one hour when the taps A and B are open = (1/12)+(1/15)= 9/60= 3/20.
Tank filled in one hour when the taps A and C are open = (1/12) + (1/20) = 8/60 = 2/15
Therefore, part of the tank filled in two hours = (3/20) + (2/15) = 17/60.
Part filled in 6 hours = ( 17/60) * 3 = 51/60
Remaining part = 9/60 = 3/20After 6 hours Now it is (A+B)’s turn
Time taken by the A+B to fill 3/20 part = 1 hour
Therefore, total time taken = 6+1 = 7 hoursHence, option (d) is correct.
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Question 5 of 5
5. Question
Amit can row 8 km/hr in still water. If the river is flowing at 4 km/hr, it takes 1.5 hours to row to a place and back. How far is the place?
Correct
Solution: A
It is given that: Speed in still water = 8 km/hr
Speed of the stream = 4 km/hrSpeed of upstream = (8-4) = 4 km/hr
Speed of downstream = (8+4) = 12 km/hr
Total time = 1.5 hrs
Let x is the distance.Then substituting the values, we get
è x/12 + x/4 = 3/2
x = 4.5 kmHence, option (a) is correct.
Direction for the following 5 (five) items: Consider the given information and answer the five items that follow:
The given bar graph shows the number of mobile users of three brands
(LG, Samsung and Nokia) in different cities. The table shows the percentage of Females among these mobile users.
Incorrect
Solution: A
It is given that: Speed in still water = 8 km/hr
Speed of the stream = 4 km/hrSpeed of upstream = (8-4) = 4 km/hr
Speed of downstream = (8+4) = 12 km/hr
Total time = 1.5 hrs
Let x is the distance.Then substituting the values, we get
è x/12 + x/4 = 3/2
x = 4.5 kmHence, option (a) is correct.
Direction for the following 5 (five) items: Consider the given information and answer the five items that follow:
The given bar graph shows the number of mobile users of three brands
(LG, Samsung and Nokia) in different cities. The table shows the percentage of Females among these mobile users.
