UPSC Insta–DART (Daily Aptitude and Reasoning Test) 2 Oct 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 Adarsh, Bala and Khonda start from the same place and travel in the same direction at speeds of 15, 30 and 60 km per hour respectively. Bala starts two hours after Adarsh. If Bala and Khonda overtake Adarsh at the same instant, how many hours after Adarsh did Khonda start? a) 4 hrs b) 2 hrs c) 3 hrs d) 6 hrs Correct Answer: Option (c) Explanation: Let us assume that Adarsh started running at 10 AM and Bala started at 12 noon. So, in these two hours’ distance travelled by Adarsh is 30 km and the relative speed of Bala with respect to Adarsh is 15 km/hr. So Bala will overtake Adarsh after =30/15 =2 hrs So, Bala reaches there at 2 PM. So, Khonda also overtakes Adarsh at 2 PM. Let us assume Khonda takes t time to overtake Adarsh and the relative speed of Khonda with respect to Adarsh is 45 km/hr and Adarsh ran for 4 hrs. So, distance travelled by Adarsh is: = time × speed = 4 × 45 ……. (i) While Khonda’s distance travelled is: =t × 60 ——– (ii) Since distance travelled by them is equal, ⇒ (i) = (ii) ⇒ 4 × 45 = t × 60 T = 3 hours So, after 3 hrs, Khonda will start running. Hence option (c) is the correct answer. Incorrect Answer: Option (c) Explanation: Let us assume that Adarsh started running at 10 AM and Bala started at 12 noon. So, in these two hours’ distance travelled by Adarsh is 30 km and the relative speed of Bala with respect to Adarsh is 15 km/hr. So Bala will overtake Adarsh after =30/15 =2 hrs So, Bala reaches there at 2 PM. So, Khonda also overtakes Adarsh at 2 PM. Let us assume Khonda takes t time to overtake Adarsh and the relative speed of Khonda with respect to Adarsh is 45 km/hr and Adarsh ran for 4 hrs. So, distance travelled by Adarsh is: = time × speed = 4 × 45 ……. (i) While Khonda’s distance travelled is: =t × 60 ——– (ii) Since distance travelled by them is equal, ⇒ (i) = (ii) ⇒ 4 × 45 = t × 60 T = 3 hours So, after 3 hrs, Khonda will start running. Hence option (c) is the correct answer.
#### 1. Question
Adarsh, Bala and Khonda start from the same place and travel in the same direction at speeds of 15, 30 and 60 km per hour respectively. Bala starts two hours after Adarsh. If Bala and Khonda overtake Adarsh at the same instant, how many hours after Adarsh did Khonda start?
Answer: Option (c)
Explanation:
Let us assume that Adarsh started running at 10 AM and Bala started at 12 noon.
So, in these two hours’ distance travelled by Adarsh is 30 km and the relative speed of Bala with respect to Adarsh is 15 km/hr.
So Bala will overtake Adarsh after =30/15 =2 hrs
So, Bala reaches there at 2 PM.
So, Khonda also overtakes Adarsh at 2 PM.
Let us assume Khonda takes t time to overtake Adarsh and the relative speed of Khonda with respect to Adarsh is 45 km/hr and Adarsh ran for 4 hrs.
So, distance travelled by Adarsh is:
= time × speed
= 4 × 45 ……. (i)
While Khonda’s distance travelled is:
=t × 60 ——– (ii)
Since distance travelled by them is equal,
⇒ (i) = (ii)
⇒ 4 × 45 = t × 60
T = 3 hours So, after 3 hrs, Khonda will start running. Hence option (c) is the correct answer.
Answer: Option (c)
Explanation:
Let us assume that Adarsh started running at 10 AM and Bala started at 12 noon.
So, in these two hours’ distance travelled by Adarsh is 30 km and the relative speed of Bala with respect to Adarsh is 15 km/hr.
So Bala will overtake Adarsh after =30/15 =2 hrs
So, Bala reaches there at 2 PM.
So, Khonda also overtakes Adarsh at 2 PM.
Let us assume Khonda takes t time to overtake Adarsh and the relative speed of Khonda with respect to Adarsh is 45 km/hr and Adarsh ran for 4 hrs.
So, distance travelled by Adarsh is:
= time × speed
= 4 × 45 ……. (i)
While Khonda’s distance travelled is:
=t × 60 ——– (ii)
Since distance travelled by them is equal,
⇒ (i) = (ii)
⇒ 4 × 45 = t × 60
T = 3 hours So, after 3 hrs, Khonda will start running. Hence option (c) is the correct answer.
• Question 2 of 5 2. Question Alok and Rudra started from two places Gadag and Dharwad towards Dharwad and Gadag respectively at 8:20am. The speeds of Alok and Rudra are in the ratio 4:5. They meet at Hubli Channamma Circle, somewhere between Gadag and Dharwad spent some time together for coffee and burger and then both started towards their destination at 9:27 am. If Alok reaches Dharwad at 10:32 am, how much time did they spend together? a) 60 minutes b) 20 minutes c) 15 minutes d) 30 minutes Correct Answer: Option (c) Explanation: Time taken by Alok to travel from the meeting point to Dharwad, =10:32 am − 9:27 am = 1 hr 5 min Speed of Alok and Rudra = 4: 5 Since time is inversely proportional to speed, time taken by Rudra to travel from Dharwad to the meeting point = (1 hr 5 min) × 4/5 = 48 + 4 = 52 min Therefore, time at which they both reached the meeting point = 8:20 am + 52 min = 9:12 am Time that they spent together for coffee and burger = 9:27 am − 9:12 am = 15 minutes. Hence, option (c) is the correct answer. Incorrect Answer: Option (c) Explanation: Time taken by Alok to travel from the meeting point to Dharwad, =10:32 am − 9:27 am = 1 hr 5 min Speed of Alok and Rudra = 4: 5 Since time is inversely proportional to speed, time taken by Rudra to travel from Dharwad to the meeting point = (1 hr 5 min) × 4/5 = 48 + 4 = 52 min Therefore, time at which they both reached the meeting point = 8:20 am + 52 min = 9:12 am Time that they spent together for coffee and burger = 9:27 am − 9:12 am = 15 minutes. Hence, option (c) is the correct answer.
#### 2. Question
Alok and Rudra started from two places Gadag and Dharwad towards Dharwad and Gadag respectively at 8:20am. The speeds of Alok and Rudra are in the ratio 4:5. They meet at Hubli Channamma Circle, somewhere between Gadag and Dharwad spent some time together for coffee and burger and then both started towards their destination at 9:27 am. If Alok reaches Dharwad at 10:32 am, how much time did they spend together?
• a) 60 minutes
• b) 20 minutes
• c) 15 minutes
• d) 30 minutes
Answer: Option (c)
Explanation:
Time taken by Alok to travel from the meeting point to Dharwad,
=10:32 am − 9:27 am = 1 hr 5 min Speed of Alok and Rudra = 4: 5
Since time is inversely proportional to speed, time taken by Rudra to travel from Dharwad to the meeting point = (1 hr 5 min) × 4/5 = 48 + 4 = 52 min
Therefore, time at which they both reached the meeting point = 8:20 am + 52 min = 9:12 am
Time that they spent together for coffee and burger = 9:27 am − 9:12 am = 15 minutes. Hence, option (c) is the correct answer.
Answer: Option (c)
Explanation:
Time taken by Alok to travel from the meeting point to Dharwad,
=10:32 am − 9:27 am = 1 hr 5 min Speed of Alok and Rudra = 4: 5
Since time is inversely proportional to speed, time taken by Rudra to travel from Dharwad to the meeting point = (1 hr 5 min) × 4/5 = 48 + 4 = 52 min
Therefore, time at which they both reached the meeting point = 8:20 am + 52 min = 9:12 am
Time that they spent together for coffee and burger = 9:27 am − 9:12 am = 15 minutes. Hence, option (c) is the correct answer.
• Question 3 of 5 3. Question Two cities Rampur and Dhamnagar are 300 km apart, Bhavya starts from Rampur at 8 : 24 am and an hour later Abhi starts from same city. After travelling for one hour Abhi reaches at city which Bhavya had passed 40 min earlier. The city is in the way of Rampur and Dhamnagar. If they reaches city Dhamnagar at same time. Find their speed. a) 50 km/hr, 75 km/hr b) 75 km/hr, 75 km/hr c) 100 km/hr, 100 km/hr d) 75 km/hr, 100 km/hr Correct Answer: Option (d) Explanation: Let the city in way of Rampur and Dhamnagar is C. Time Speed Bhavya 80 3x Abhi 60 4x 300/3x) – (300/4x) = 1 25/x = 1 ⇒ x = 25 ∴ Bhavya Speed = 3 × 25 = 75 km/hr Abhi speed = 4 × 25 = 100 km/hr Hence, option (d) is correct answer. Incorrect Answer: Option (d) Explanation: Let the city in way of Rampur and Dhamnagar is C. Time Speed Bhavya 80 3x Abhi 60 4x 300/3x) – (300/4x) = 1 25/x = 1 ⇒ x = 25 ∴ Bhavya Speed = 3 × 25 = 75 km/hr Abhi speed = 4 × 25 = 100 km/hr Hence, option (d) is correct answer.
#### 3. Question
Two cities Rampur and Dhamnagar are 300 km apart, Bhavya starts from Rampur at 8 : 24 am and an hour later Abhi starts from same city. After travelling for one hour Abhi reaches at city which Bhavya had passed 40 min earlier. The city is in the way of Rampur and Dhamnagar. If they reaches city Dhamnagar at same time. Find their speed.
• a) 50 km/hr, 75 km/hr
• b) 75 km/hr, 75 km/hr
• c) 100 km/hr, 100 km/hr
• d) 75 km/hr, 100 km/hr
Answer: Option (d)
Explanation:
Let the city in way of Rampur and Dhamnagar is C.
Time Speed
Bhavya 80 3x
Abhi 60 4x
300/3x) – (300/4x) = 1
25/x = 1 ⇒ x = 25
∴ Bhavya Speed = 3 × 25 = 75 km/hr
Abhi speed = 4 × 25 = 100 km/hr Hence, option (d) is correct answer.
Answer: Option (d)
Explanation:
Let the city in way of Rampur and Dhamnagar is C.
Time Speed
Bhavya 80 3x
Abhi 60 4x
300/3x) – (300/4x) = 1
25/x = 1 ⇒ x = 25
∴ Bhavya Speed = 3 × 25 = 75 km/hr
Abhi speed = 4 × 25 = 100 km/hr Hence, option (d) is correct answer.
• Question 4 of 5 4. Question An inlet pipe A can fill water at the rate of 5 litres per minute and a leakage find in the bottom of a tank which can empty the full tank in 8 hours. When the tank is full, the inlet pipe A is opened and due to the leak the tank is empty in 12 hours. What is the capacity of the tank? (In litres) a) 6400 litres b) 6800 litres c) 7000 litres d) 7200 litres Correct Answer: Option (d) Explanation: Leakage = 8 hours (empty) Inlet pipe –leakage = 12 hours (empty) LCM = 24 units Units per hour Leakage = 3 (empty) Inlet pipe –leakage = 2 (empty) Pipe A = 3–2 = 1 unit Time to fill by Pipe A = 24/1 = 24 hours Filling rate = 5 litres per minute Total capacity = 24×5×60 = 7200 litres Hence, option (d) is correct answer. Incorrect Answer: Option (d) Explanation: Leakage = 8 hours (empty) Inlet pipe –leakage = 12 hours (empty) LCM = 24 units Units per hour Leakage = 3 (empty) Inlet pipe –leakage = 2 (empty) Pipe A = 3–2 = 1 unit Time to fill by Pipe A = 24/1 = 24 hours Filling rate = 5 litres per minute Total capacity = 24×5×60 = 7200 litres Hence, option (d) is correct answer.
#### 4. Question
An inlet pipe A can fill water at the rate of 5 litres per minute and a leakage find in the bottom of a tank which can empty the full tank in 8 hours. When the tank is full, the inlet pipe A is opened and due to the leak the tank is empty in 12 hours. What is the capacity of the tank? (In litres)
• a) 6400 litres
• b) 6800 litres
• c) 7000 litres
• d) 7200 litres
Answer: Option (d)
Explanation:
Leakage = 8 hours (empty)
Inlet pipe –leakage = 12 hours (empty)
LCM = 24 units
Units per hour
Leakage = 3 (empty)
Inlet pipe –leakage = 2 (empty)
Pipe A = 3–2 = 1 unit
Time to fill by Pipe A = 24/1 = 24 hours
Filling rate = 5 litres per minute
Total capacity = 24×5×60 = 7200 litres Hence, option (d) is correct answer.
Answer: Option (d)
Explanation:
Leakage = 8 hours (empty)
Inlet pipe –leakage = 12 hours (empty)
LCM = 24 units
Units per hour
Leakage = 3 (empty)
Inlet pipe –leakage = 2 (empty)
Pipe A = 3–2 = 1 unit
Time to fill by Pipe A = 24/1 = 24 hours
Filling rate = 5 litres per minute
Total capacity = 24×5×60 = 7200 litres Hence, option (d) is correct answer.
• Question 5 of 5 5. Question Two pipes A & B can fill a cistern in 18 min and 27 min respectively. If both pipers are opened and A is turned off after x minutes then the cistern will be filled in just 16 min. Find the value of x. a) 4 min b) 5 min c) 6 min d) 7 min Correct Answer: Option (c) Explanation: Pipe A = 18 min Pipe B = 24 min LCM = 72 units Pipe A = 4 units (fill) Pipe B = 3 units (fill) Together = 7 units (fill) B worked for whole the time 4 × x + 16×3 = 72 4x = 72–48 x = 24/4 x = 6 min Hence, option (c) is correct answer. Incorrect Answer: Option (c) Explanation: Pipe A = 18 min Pipe B = 24 min LCM = 72 units Pipe A = 4 units (fill) Pipe B = 3 units (fill) Together = 7 units (fill) B worked for whole the time 4 × x + 16×3 = 72 4x = 72–48 x = 24/4 x = 6 min Hence, option (c) is correct answer.
#### 5. Question
Two pipes A & B can fill a cistern in 18 min and 27 min respectively. If both pipers are opened and A is turned off after x minutes then the cistern will be filled in just 16 min. Find the value of x.
Answer: Option (c)
Explanation:
Pipe A = 18 min
Pipe B = 24 min
LCM = 72 units
Pipe A = 4 units (fill)
Pipe B = 3 units (fill)
Together = 7 units (fill)
B worked for whole the time 4 × x + 16×3 = 72
4x = 72–48
x = 6 min Hence, option (c) is correct answer.
Answer: Option (c)
Explanation:
Pipe A = 18 min
Pipe B = 24 min
LCM = 72 units
Pipe A = 4 units (fill)
Pipe B = 3 units (fill)
Together = 7 units (fill)
B worked for whole the time 4 × x + 16×3 = 72
4x = 72–48
x = 6 min Hence, option (c) is correct answer.
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