UPSC Insta–DART (Daily Aptitude and Reasoning Test) 4 Nov 2024
Kartavya Desk Staff
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.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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• Question 1 of 5 1. Question A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B? a) 170 km b) 160 km c) 180 km d) 190 km Correct Answer: C Explanation Speed in downstream = (14 + 4) km/hr = 18 km/hr; Speed in upstream = (14 – 4) km/hr = 10 km/hr. Let the distance between A and B be x km. Then, x/18 + (x/2)/10 = 19 ⇔ x/18 + x/20 = 19 ⇒ x = 180 km. Incorrect Answer: C Explanation Speed in downstream = (14 + 4) km/hr = 18 km/hr; Speed in upstream = (14 – 4) km/hr = 10 km/hr. Let the distance between A and B be x km. Then, x/18 + (x/2)/10 = 19 ⇔ x/18 + x/20 = 19 ⇒ x = 180 km.
#### 1. Question
A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?
Explanation
Speed in downstream = (14 + 4) km/hr = 18 km/hr;
Speed in upstream = (14 – 4) km/hr = 10 km/hr.
Let the distance between A and B be x km. Then,
x/18 + (x/2)/10 = 19 ⇔ x/18 + x/20 = 19 ⇒ x = 180 km.
Explanation
Speed in downstream = (14 + 4) km/hr = 18 km/hr;
Speed in upstream = (14 – 4) km/hr = 10 km/hr.
Let the distance between A and B be x km. Then,
x/18 + (x/2)/10 = 19 ⇔ x/18 + x/20 = 19 ⇒ x = 180 km.
• Question 2 of 5 2. Question Rajani rows in still water with a speed of 4.5 kmph to go to a certain place and to come back . Find his average speed for the whole journey , if the river is flowing with a speed of 1.5 kmph ? a) 8 kmph b) 4 kmph c) 5 kmph d) 6 kmph Correct Answer: B Explanation Rajani’s speed upstream = 4.5 – 1.5 = 3 kmph Rajani’s speed downstream = 4.5+1.5 = 6 kmph Distance = X km Time Taken in upstream = X/3 Time Taken in downstream = X/6 Average Speed = 2X/(X/3 + X/6 ) = 4 kmph Incorrect Answer: B Explanation Rajani’s speed upstream = 4.5 – 1.5 = 3 kmph Rajani’s speed downstream = 4.5+1.5 = 6 kmph Distance = X km Time Taken in upstream = X/3 Time Taken in downstream = X/6 Average Speed = 2X/(X/3 + X/6 ) = 4 kmph
#### 2. Question
Rajani rows in still water with a speed of 4.5 kmph to go to a certain place and to come back . Find his average speed for the whole journey , if the river is flowing with a speed of 1.5 kmph ?
Explanation
Rajani’s speed upstream = 4.5 – 1.5 = 3 kmph
Rajani’s speed downstream = 4.5+1.5 = 6 kmph
Distance = X km
Time Taken in upstream = X/3
Time Taken in downstream = X/6
Average Speed = 2X/(X/3 + X/6 ) = 4 kmph
Explanation
Rajani’s speed upstream = 4.5 – 1.5 = 3 kmph
Rajani’s speed downstream = 4.5+1.5 = 6 kmph
Distance = X km
Time Taken in upstream = X/3
Time Taken in downstream = X/6
Average Speed = 2X/(X/3 + X/6 ) = 4 kmph
• Question 3 of 5 3. Question The distance between two stations A and B is 246 km. A train starts from A move towards B at an average speed of 24 kmph. Another train starts from B, 10 minutes earlier than the train at A and moves towards A at an average of 36 kmph. How far from A will the two trains meet?(approx.) a) 96 km b) 80 km c) 120 km d) 190 km Correct Answer: A Explanation Let the trains meets at a distance of x km from A. After 10 mins, remaining distance = 246 – (36 1/6) = 240 km At the time they meet = 240/(24 + 36) = 4 hrs Required distance = 4 24 = 96 km Incorrect Answer: A Explanation Let the trains meets at a distance of x km from A. After 10 mins, remaining distance = 246 – (36 1/6) = 240 km At the time they meet = 240/(24 + 36) = 4 hrs Required distance = 4 24 = 96 km
#### 3. Question
The distance between two stations A and B is 246 km. A train starts from A move towards B at an average speed of 24 kmph. Another train starts from B, 10 minutes earlier than the train at A and moves towards A at an average of 36 kmph. How far from A will the two trains meet?(approx.)
Explanation
Let the trains meets at a distance of x km from A.
After 10 mins, remaining distance = 246 – (36 * 1/6) = 240 km
At the time they meet = 240/(24 + 36) = 4 hrs
Required distance = 4 * 24 = 96 km
Explanation
Let the trains meets at a distance of x km from A.
After 10 mins, remaining distance = 246 – (36 * 1/6) = 240 km
At the time they meet = 240/(24 + 36) = 4 hrs
Required distance = 4 * 24 = 96 km
• Question 4 of 5 4. Question Train A crosses train B running in same direction in 60 seconds and train B crosses a pole in 8 seconds. If the ratio of the length of train A to B is 3:2 and train B is faster than A, then find the speed of train A? a) 40 kmph b) 60 kmph c) 90 kmph d) Cannot be determine Correct Answer: D Explanation Length of train A = 3x Length of train B = 2x Speed of train A = a Speed of train B = b 3x + 2x = (b – a) 5/18 60 3x = 10b – 10a 2x = b 5/18 8 9x = 10b Hence, we cannot find the answer Incorrect Answer: D Explanation Length of train A = 3x Length of train B = 2x Speed of train A = a Speed of train B = b 3x + 2x = (b – a) 5/18 60 3x = 10b – 10a 2x = b 5/18 8 9x = 10b Hence, we cannot find the answer
#### 4. Question
Train A crosses train B running in same direction in 60 seconds and train B crosses a pole in 8 seconds. If the ratio of the length of train A to B is 3:2 and train B is faster than A, then find the speed of train A?
• a) 40 kmph
• b) 60 kmph
• c) 90 kmph
• d) Cannot be determine
Explanation
Length of train A = 3x
Length of train B = 2x
Speed of train A = a
Speed of train B = b
3x + 2x = (b – a) 5/18 60
3x = 10b – 10a
2x = b 5/18 8
9x = 10b Hence, we cannot find the answer
Explanation
Length of train A = 3x
Length of train B = 2x
Speed of train A = a
Speed of train B = b
3x + 2x = (b – a) 5/18 60
3x = 10b – 10a
2x = b 5/18 8
9x = 10b Hence, we cannot find the answer
• Question 5 of 5 5. Question The time taken by the Train to cross a platform of length 200 m is 30 seconds and to cross an electric pole in 20 seconds. Find the speed of the train in km/hr. a) 72 km/hr b) 54 km/hr c) 45 km/hr d) 36 km/hr Correct Answer: A Explanation Length of the train = x Time taken by the Train to cross a platform of length 200 m is 30 seconds Speed of the train = (x+200)/30 —– (1) Time taken by the Train to cross an electric pole Speed of the train = x/20 —– (2) From (1) and (2) (x+200)/30 = x/20 2x + 400 = 3x x = 400m Speed of the Train = 400/20 = 20 m/s = 2018/5 = 72 km/hr Incorrect Answer: A Explanation Length of the train = x Time taken by the Train to cross a platform of length 200 m is 30 seconds Speed of the train = (x+200)/30 —– (1) Time taken by the Train to cross an electric pole Speed of the train = x/20 —– (2) From (1) and (2) (x+200)/30 = x/20 2x + 400 = 3x x = 400m Speed of the Train = 400/20 = 20 m/s = 2018/5 = 72 km/hr
#### 5. Question
The time taken by the Train to cross a platform of length 200 m is 30 seconds and to cross an electric pole in 20 seconds. Find the speed of the train in km/hr.
• a) 72 km/hr
• b) 54 km/hr
• c) 45 km/hr
• d) 36 km/hr
Explanation
Length of the train = x
Time taken by the Train to cross a platform of length 200 m is 30 seconds
Speed of the train = (x+200)/30 —– (1)
Time taken by the Train to cross an electric pole
Speed of the train = x/20 —– (2)
From (1) and (2)
(x+200)/30 = x/20
2x + 400 = 3x
Speed of the Train = 400/20 = 20 m/s = 20*18/5 = 72 km/hr
Explanation
Length of the train = x
Time taken by the Train to cross a platform of length 200 m is 30 seconds
Speed of the train = (x+200)/30 —– (1)
Time taken by the Train to cross an electric pole
Speed of the train = x/20 —– (2)
From (1) and (2)
(x+200)/30 = x/20
2x + 400 = 3x
Speed of the Train = 400/20 = 20 m/s = 20*18/5 = 72 km/hr
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