UPSC Insta–DART (Daily Aptitude and Reasoning Test) 7 Nov 2024

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 can travel 3.5km upstream in 14min. If the ratio of the speed of the boat in still water to the speed of the stream is 7:2. How much time will the boat take to cover 36km downstream ? a) 65min b) 80min c) 75min d) 70min Correct Answer: B Solution: Speed = 7x:2x Downstream = 9x; upstream = 5x Upstream speed = 3.560/14 = 15kmph 5x = 15 x = 3 Downstream = 93 = 27 Time taken for 36km = 3660/27 = 80min Incorrect Answer: B Solution: Speed = 7x:2x Downstream = 9x; upstream = 5x Upstream speed = 3.560/14 = 15kmph 5x = 15 x = 3 Downstream = 93 = 27 Time taken for 36km = 3660/27 = 80min

#### 1. Question

A boat can travel 3.5km upstream in 14min. If the ratio of the speed of the boat in still water to the speed of the stream is 7:2. How much time will the boat take to cover 36km downstream ?

Speed = 7x:2x

Downstream = 9x; upstream = 5x

Upstream speed = 3.5*60/14 = 15kmph

Downstream = 9*3 = 27

Time taken for 36km = 36*60/27 = 80min

Speed = 7x:2x

Downstream = 9x; upstream = 5x

Upstream speed = 3.5*60/14 = 15kmph

Downstream = 9*3 = 27

Time taken for 36km = 36*60/27 = 80min

• Question 2 of 5 2. Question There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 6 km/hr, While the other sails on a boat at a speed of 8 km/hr. If the river flows at the speed of 6 km/hr, which of the two friends will return to place A first? a) Cyclist b) Sailor c) Both come at same time d) Anyother Correct Answer: A Solution: Average speed of the cyclist =6 km/hr Downstream speed=8+6=14 km/hr Upstream speed =8−6=2 km/hr Therefore, average speed of the sailor =2142/(14+2) =3.5km/hr Average speed of the cyclist is more than that of the sailor. Therefore, the cyclist will return first. Incorrect Answer: A Solution: Average speed of the cyclist =6 km/hr Downstream speed=8+6=14 km/hr Upstream speed =8−6=2 km/hr Therefore, average speed of the sailor =2142/(14+2) =3.5km/hr Average speed of the cyclist is more than that of the sailor. Therefore, the cyclist will return first.

#### 2. Question

There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 6 km/hr, While the other sails on a boat at a speed of 8 km/hr. If the river flows at the speed of 6 km/hr, which of the two friends will return to place A first?

• a) Cyclist

• c) Both come at same time

• d) Anyother

Average speed of the cyclist =6 km/hr

Downstream speed=8+6=14 km/hr

Upstream speed =8−6=2 km/hr

Therefore, average speed of the sailor

=2142/(14+2)

Average speed of the cyclist is more than that of the sailor. Therefore, the cyclist will return first.

Average speed of the cyclist =6 km/hr

Downstream speed=8+6=14 km/hr

Upstream speed =8−6=2 km/hr

Therefore, average speed of the sailor

=2142/(14+2)

Average speed of the cyclist is more than that of the sailor. Therefore, the cyclist will return first.

• Question 3 of 5 3. 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? a) 210km b) 185km c) 140km d) 168km Correct Answer: D Solution: Downstream speed = 10+4 = 14 Upstream speed = 10-4 = 6 Now total time is 26 hours If distance between A and B is d, then distance BC = d/2 Now distance/speed = time, so d/14 + (d/2)/6= 26 13d/84=26 Solve, d = 168 km Incorrect Answer: D Solution: Downstream speed = 10+4 = 14 Upstream speed = 10-4 = 6 Now total time is 26 hours If distance between A and B is d, then distance BC = d/2 Now distance/speed = time, so d/14 + (d/2)/6= 26 13d/84=26 Solve, d = 168 km

#### 3. 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?

Downstream speed = 10+4 = 14

Upstream speed = 10-4 = 6

Now total time is 26 hours

If distance between A and B is d, then distance BC = d/2

Now distance/speed = time, so

d/14 + (d/2)/6= 26

Solve, d = 168 km

Downstream speed = 10+4 = 14

Upstream speed = 10-4 = 6

Now total time is 26 hours

If distance between A and B is d, then distance BC = d/2

Now distance/speed = time, so

d/14 + (d/2)/6= 26

Solve, d = 168 km

• Question 4 of 5 4. Question Two stations P and Q are 240 km apart on a straight line. One train starts from P at 4 p.m. and travels towards at 15 kmph. Another train starts from Q at 5 p.m. and travels towards P at a speed of 30 kmph. At what time will they meet? a) 10:45 p.m b) 11 p.m. c) 10 p.m. d) 11:45 p.m. Correct Answer: C Solution: Let they meet x hours after 4 pm. Distance covered by P in x hours = 20x km. Distance covered by Q in (x – 1) hours = 25(x – 1) km. Therefore, 15x + 30(x – 1) = 240 =>45x = 270 => x = 6 So, they meet at 10 p.m. Incorrect Answer: C Solution: Let they meet x hours after 4 pm. Distance covered by P in x hours = 20x km. Distance covered by Q in (x – 1) hours = 25(x – 1) km. Therefore, 15x + 30(x – 1) = 240 =>45x = 270 => x = 6 So, they meet at 10 p.m.

#### 4. Question

Two stations P and Q are 240 km apart on a straight line. One train starts from P at 4 p.m. and travels towards at 15 kmph. Another train starts from Q at 5 p.m. and travels towards P at a speed of 30 kmph. At what time will they meet?

• a) 10:45 p.m

• b) 11 p.m.

• c) 10 p.m.

• d) 11:45 p.m.

Let they meet x hours after 4 pm.

Distance covered by P in x hours = 20x km.

Distance covered by Q in (x – 1) hours = 25(x – 1) km.

Therefore, 15x + 30(x – 1) = 240

=>45x = 270

So, they meet at 10 p.m.

Let they meet x hours after 4 pm.

Distance covered by P in x hours = 20x km.

Distance covered by Q in (x – 1) hours = 25(x – 1) km.

Therefore, 15x + 30(x – 1) = 240

=>45x = 270

So, they meet at 10 p.m.

• Question 5 of 5 5. Question A train departs Kolkata at 6 a.m. at a speed of 40 kmph. After one hour, another train departs Kolkata in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Kolkata do the two trains meet? a) 200km b) 210km c) 240km d) 205km Correct Answer: A Solution: When the second train departs Kolkata the first train covers 40 1 = 40 km So, the distance between first train and second train is 40 km at 7.00am Time taken by the trains to meet = Distance / relative speed = 40 / (50 -40) = 4 hours So, the two trains meet at 10 a.m. The two trains meet 4 50 = 200 km away from Kolkata. Incorrect Answer: A Solution: When the second train departs Kolkata the first train covers 40 1 = 40 km So, the distance between first train and second train is 40 km at 7.00am Time taken by the trains to meet = Distance / relative speed = 40 / (50 -40) = 4 hours So, the two trains meet at 10 a.m. The two trains meet 4 50 = 200 km away from Kolkata.

#### 5. Question

A train departs Kolkata at 6 a.m. at a speed of 40 kmph. After one hour, another train departs Kolkata in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Kolkata do the two trains meet?

When the second train departs Kolkata the first train covers 40 * 1 = 40 km

So, the distance between first train and second train is 40 km at 7.00am

Time taken by the trains to meet = Distance / relative speed

= 40 / (50 -40) = 4 hours

So, the two trains meet at 10 a.m.

The two trains meet 4 * 50 = 200 km away from Kolkata.